Note: This does not directly answer the question, but can serve as a starting point for the research, which is why I'm leaving it here for now. The numbers being asked for may not have ever been gathered and analyzed, but if they have, they don't seem to be in the linked-to study.
I found a summary of a 2006 report on how long SNAP participants receive benefits, which has a chart which somewhat your question for August 1990 - October 1999.
I haven't been able to track down a more recent study, but for that decade only 21% of the people stayed on for more than two years after joining the program. From the report:
Among all individuals participating in March 1996, SIPP data suggest that half were in the middle of participation spells lasting four and a half years or longer, while FSPQC data indicate that only one-third of the caseload was in the middle of spells of at least four and a half years. In FSPQC data, the median participation spell for March 1996 participants was just over two years. While it is unclear why the estimates from these separate sources differ, it appears that the estimated median participation spell of eight years for a cross-section of FSP participants is no longer an accurate depiction of the FSP dynamics.