Hmm, what's strange about your ISP's recommendation is that when questioned about the DSL connection dropping, he recommends a change in router. Well isn't it the modem (or at least the modem portion of the combination modem+router (I assume that's what you have) that's dropping the DSL connection, and not the router? Or perhaps it's not really dropping the DSL connection at all, but some other router-specific issue, like not enough capacity to manage the traffic.
Anyway, there are "gaming routers" out there, they’re even marketed as such. Just search Google and I'm sure you'll find plenty of them. Perhaps someone else will have a specific recommendation, but frankly I'd just check the reviews. There are so many variables that you might want to consider, such as are you using a wired or wireless connection, G or N (assuming wireless), single or dual band, gigabit or just 10/100mbps, etc.