Recently I started to have some problems with my network connection. After a little time (from 5 to 45 minutes) the connection seemed somewhat dropped. My ISP says that the physical DSL connection is completely fine. The connection between my router and my modem also looks fine. The connection between my PC and my router seems to work too. (I'm not on Wi-Fi.) My router doesn't dial in again. It's just that all my downloads, IM connections and everything like that ceases to be.
I tried to connect trough the modem directly from a PC. If I do that I can't reproduce the issue, the TCP connections remain alive for more than an hour. Because of this my ISP says it's not their problem, it's the router's. I somewhat doubt that because I can reproduce it with two completely different routers. (I have a Belkin and a TP-Link router to try.) I also tried the ideas Google brought up, like making sure that my firmware is up to date and praying that it will work. Without any luck.
Now the question is: how can I test out what problems the router (but no PCs) see with my connection (or vice versa why problem does my connection have with routers but no PCs)? My router logs are not very informative on that part since there is usually no physical disconnection and re-dial. I would really prefer a thorough deterministic way that actually gives me the result over guesswork, because if it really is my ISP's problem I'll need hard evidence to make them work for their money. (And no, sadly simply changing my ISP isn't an option.)