Hello there!
Now.. I am not an expert here, but I have had similar problems as you. I called my DSL service provider, and they helped out on this.
I have had problems twice. Once it was due to having the telephone line going through a power surge protector that was not working properly. I plugged it in directly, and fixed that problem.
The other time I had a problem with the router. So, I bypassed the router and went straight into the network card. Problem solved. My memory is fuzzy on this one, but I believe I had to reload the software for the router; there was something that got corrupted on it. I assume you have done a full power down of the router, and then brought it back up. Are all the modem lights on in the correct sequence/ timing that they should be (assuming your modem has such lights)?
Anyway, you might consider bypassing a telephone surge protector (if you have one), and bypassing the router to see if your issues are due to it. If so, then you can diagnose what problem it may be contributing.
Just some thoughts.