Wikipedia never explained why he didn't get the chance to play in Russia again. Western countries holding him "hostage?" Russia not wanting expressive musicians in their country? I don't know.
He was opposed to the revolution, and moved to America in 1917.
On January 15, 1931 Rachmaninoff (soon after he had finished a European concert tour) and a couple other Russian immigrants signed a letter in the New York Times criticizing Soviet Russia:
[...] all Russia is groaning under the terrible yoke of a numerically negligible but well-organized gang of Communists intent on reducing the peasants to a state of abject misery and that these unfortunate sufferers are being daily and systematically subjected to indescribable privations, humiliations and torture. At no time, in no country, has there ever existed a government responsible for so many cruelties, wholesale murders, and common-law crimes in general.
He was censured in a number of Russian newspapers (e.g. Vechernaya Moskva & Pravda) In response to the letter, the performance of his music was banned in the Soviet Union, which was only later lifted in 1933 after Roosevelt resumed diplomatic relations with the Soviet Union.
In any case, his choice not to return to Russia was due to his political animosity for the USSR.