There is a lot you theoretically can do - but it depends things like your hardware etc.
- create PING sensors - interval 30 seconds - PING targets should be various web-sites like google.com etc.. - just to have a broader picture
- PING the provider primary gateway after your router
- PING the provider secondary gateway, assuming you have one and know it (TRACERT / TRACEROUTE)
- PING your router internally
If your router supports it - use SNMP - in two ways if possible:
- PRTG sends SNMP queries to your router (top interval 30 seconds)
- PRTG is the trap target for SNMP generated log-messages from your router (this is pro-active from the router)
You further mention you don't see anything in your router logs - this is rather confusing. I highly recommend to investigate your internal structure as well.
Without knowing more details about your network, I can only guess around on what is the root cause. If you really think it is an provider issue then probably start using PINGPLOTTER for a while and see where the connection drop occurs and when - this might be helpful for you as well cause it shows the hops down the line.
Hope this points you in the right direction and is all helpful to you