Japan was never isolated from China in terms of trade but there were long periods of no official governmental contact between the two countries. So the premise needs to be better defined.

Here's the long story:

Direct government to government contact started very early on since the 1st century AD. For example: here's a gold seal from Emperor Guangwu of the Later Han dynasty to the Kingdom of Na in Japan.

http://en.wikipedia.org/wiki/Wa_%28Japan%29#mediaviewer/File:King_of_Na_gold_seal_faces.jpg

This government to government contact was in the form of tributary relations. In other words the rulers of Japan became the vassals of the ruler of China. In exchange when the two trade in official missions, the Chinese side gives more (to show that they are superior) than the Japanese side gives. And in theory, when something happens, the Chinese ruler must protect and defend his vassal.

This relationship ends in 605. Prince Shotoku declared in an official letter to the Chinese emperor of Sui dynasty that Japan was not a vassal state of China and that the two were equals. He used the title Child of Heaven to refer to both the Chinese and Japanese rulers.

Here's the original in classical Chinese from vol 81, Biographies no 46, Eastern Barbarians: Kingdom of Wa in the History of Sui dynasty

「日出處天子致書日沒處天子無恙云云」「卷八十一 列傳第四十六 東夷 俀國」）」

(The Chinese side understandably got upset and continued to treat the Japanese emissaries as tributary missions.)

Government to government contact continued for another 200+ years until 838. (The Japanese thinking they are equals, the Chinese thinking they are superior.) And in 894 Sugawara no Michizane officially terminated the government to government missions citing that there was nothing to learn from Tang China in decline and that they were treating the Japanese emissaries as tributary missions.

From this point onwards there is no official contact between successive Chinese governments and the Imperial government of Japan until the Meiji period (1868-1911). The Chinese under the Tang dynasty (618-906) and the Song dynasty (960-1279) did not bother to re-establish official relations with Japan. The Song in particular had bigger foreign policy problems: namely the Steppe nomads (Khitans, Jurchens, Mongols).

No contact between governments does not mean that there was no private trade. Private trade existed from the beginning of history and continued to exist throughout this period. For example, the Taira clan amassed huge wealth by trading with Chinese merchants and it supported their rise as a powerful samurai clan in Japan.

Over time, the imperial family of Japan and the high ranking aristocratic family lost power inside Japan. The samurai, led by the Minamoto clan and the Hojo clan took power and ruled Japan through the Kamakura shogunate (1192-1333). The shogun is the leader of all samurai, but technically he is appointed by the Emperor of Japan. Under the Kamakura shogunate there still was no official contact between Japan and China (but lots of private trade continued).

The Mongols who conquered China tried to change that by getting Japan to become a tributary state again. When the Kamakura samurai refused, the Mongols decided to settle this by force and invaded Japan twice (1274, 1281).

The Mongols invasions failed. Japan remained independent. However, the invasions led to the Hojo clan concentrating power and wealth inside Japan, and the other samurai revolted, ending the Kamakura shogunate. In the ensuing civil war, a weak Muromachi shogunate would arise in which the Ashikaga clan ruled Japan as the shogun.

Also Japanese "pirates" began to ply the oceans shortly after the Mongol invasions. The Mongols and their Korean and Chinese allies on the way to Kyushu, kidnapped a lot of the women and children in the islands of Tsushima and Iki. So the piracy started as a response to get these kidnapped people back.

After the Mongols lost power in China, the Ming dynasty (1368-1644) rose in China. The Ming Emperors wanted to end the piracy so they contacted the Japanese rulers. Since the Muromachi shogunate was really in charge of Japan (and the imperial government of Japan was just a shadow of its former self), the Ming contacted the shoguns of Japan. In 1404 the 3rd Muromachi shogun, Ashikaga Yoshimitsu, agreed to become a vassal of the 3rd Ming emperor, Yongle, and thus became the King of Japan. Ashikaga Yoshimitsu therefore became a vassal of the Emperor of Japan and a vassal of the Emperor of China.

Ashikaga Yoshimitsu ended the piracy off the China coast and instead re-opened the tributary trade relationship. So from 1404 to 1551, there was a tributary trade between China and Japan and also a license trade between China and Japan. Official missions from Japan to China resulted in Chinese giving more than they received (this was limited to once every ten years). And private trade between China and Japan was limited to licensed traders.

This was the only 150 years in which governments in China and in Japan had control over the trade between two countries (both official and private).

Of course limiting private trade to licensed traders meant that there were people who wanted to trade, but didn't get a license. The Ming dynasty called these unofficial traders "pirates" again, and they became a big problem again after the 1500s. So the Ming dynasty's efforts to curb piracy and control trade only lasted a hundred years.

By the late 1400s Muromachi shoguns were weak and Japan was under a period of intense civil strife: the Warring States Era (1477-1603). No authority could stop the private traders called pirates like Ashikaga Yoshimitsu did earlier.

When the Ming dynasty rescinded the vassal status of various rulers in Japan (towards the end, they gave vassal status to samurai lords) and terminated the officially licensed trade in 1551, the situation returned to the more normal state of affairs between China and Japan in pre-modern times: no government contact, lots of private trade.

When the Tokugawa clan took power in Japan in 1600 and opened the Edo shogunate (1603-1868) there was a possibility that there might be official relations between Japan and China. But in the end, there was none. Until the 1850s, the situation remained the same as before the Tokugawa took over. No government to government contact, but lots of trade between private merchants.

After the 1630s, the Edo shogunate designated Nagasaki as the only port of call for Chinese and Dutch traders and forbade Japanese traders from leaving Japan. So the 220 years between 1630s and 1850s was a strange period in which Japan isolated itself and didn't allow Japanese to leave the country. But even in this period, Chinese traders could still come to Nagasaki to trade.

After 1868, relations between China and Japan was set along Western International norms and continues to this day.

So in a nutshell official contact between the governments of Japan and China was relatively few after ancient times. From ca 100 AD to 838/894 is the longest stretch. Then 150 years from 1404 to 1551, then another 150 years from 1871 to present.

So for 500+ years from 838/894 to 1404, and then another 320 years from 1551 to 1871, there was no official contact between the governments of Japan and China. And in the case of the imperial governments of Japan and China there was no contact between 838/894 and 1871, a 1000 year break. This is pretty much unthinkable in the context of European history where diplomatic contact has been a continuous tradition since the Italian Renaissance (1400s).

It seems to me that the problem was that the Chinese insisted on being superior; and if you didn't accept that you couldn't conduct relations with them. So the only choice was to not deal with them officially.

But from earliest times to present, there was always private trade between the ordinary merchants of the two countries.