The battle itself took place in 9 AD and was one of Rome’s worst military defeats so I can understand Augustus and a few emperors after him, who had living knowledge of the defeat, wanting to keep their distance; but in the next 100 years, there wasn’t really another major invasion of the territory east of the Rhine, even when Rome was at its most expansive and taking on unified empires such as the Parthians.
Was the memory of Teutoburg forest really still alive at that point and if so did the Roman emperors really fear a confederation of German tribes more than the Parthians? If not, what kept them out of Northern Germany even at their most expansive? Was it just not appealing to them as new territory?
You may find this answer by /u/ScipioAsina helpful.
Apparently, the significance of Teutoburg is exaggerated. There are other factors that made Romans give up on Germany.
I want to correct a couple of details in the first post that are important: namely, after Teutoberg Rome never tried to annex Germania, but there were invasions east of the Rhine, and Roman commanders don't seem to have felt themselves to be kept out of Northern Germany. In fact there were retaliatory campaigns soon after Teutoberg under Germanicus that penetrated far past the Rhine and, according to Tacitus, were successful enough to put the Romans in a position where they could have annexed to the Elbe if they had wanted to. For one reason or another (or most likely, for a combination of reasons), the Romans decided they didn't want to, and while Romans kept on frequently sending soldiers into Germany when they felt like it during the following centuries (small expeditions are too numerous to name, large expeditions with imperial presence took place under Maximinus Thrax), they also kept on deciding that they didn't want to stay.
You may wish to view this question for a discussion of the Rhine's logistic advantages compared to the generally expensive to supply regions deeper in Germany.