That depends on how you define TRP. If you're talking about the subreddit itself, in ten years it will either stay as a hub for the kind of discussion about male-female relationships it provides currently, or its theories and its way of discourse will become accepted by the mainstream in a diluted form. TRP is growing because of how far it is from mainstream, and once it loses that characteristic, it dies as a distinct idea. TRP has already have significant influence on the debate outside of it, a lot of its theories and terms like "alpha fucks, beta bucks" are very common on the AskMen subreddit for example, and you can see complains about it on more feminist-inclined places on reddit. There are very few subreddits dedicated to a specific idea that are bigger than TRP - even /r/christianity is smaller now.

The reason why TRP has exploded in popularity is because it is very useful, a lot of men find it better than anything they've been offered. Which says a lot, since TRP isn't really rigorous at all when it comes to its methodology it makes some bold, but largely unfounded claims. But, it definitely helps a lot of men lead better lives. It helps fulfill men's desires to have sex with a lot of attractive women, which will always be the goal of most men, unless feminists manage to significantly alter their hormones. As long as feminism will ignore the needs of men and shame them, men will ignore and shame feminism. Yes, there are lots of people who don't need TRP to live have fulfilling relationships, but that doesn't negate the fact that a lot of people do need it, just like the fact that a lot of people have jobs doesn't negate the number of unemployed people.

I think the quality that differentiates TRP from what a lot of people are fed is that it assumes that men and women are different and tries to figure out how exactly, while the other side assumes that men and women are the same, surrendering specific differences only after the amount of evidence makes them unquestionable, after fighting them tooth and nail. The consequences of the second approach are terrible, and I suspect it's a significant reason why there are currently such significant numbers of people, both men and women, who are dissatisfied with their dating lives. These people simply don't know how the world works, they need redpill truths, they need honest debate about the nature of men and women, and they will decide what to do with the information. The TRP approach will succeed in the end, because it represents the Truth.