Something to try
You could download "The Dude" from here: MikroTik Routers and Wireless
Set it up to monitor 2 things - Your modem's IP address and a website IP address (eg. 66.102.7.99 for Google). You will see when you lose connection with just the internet or your modem.
Alternatively. If it fairly reliably goes down, go to a command prompt (Click Start ==> Run and type "cmd", then click "OK". type in "ping" and the IP address of your modem to see if you get a reply from it. If you do get a reply, there isn't an issue with your computer talking to your modem, then try pinging google if you don't get a reply you know it's an issue with your modem connecting to the net.
This is what it looks like when you successfully ping something:
C:\>ping 172.16.74.254
Pinging 172.16.74.254 with 32 bytes of data:
Reply from 172.16.74.254: bytes=32 time<1ms TTL=255
Reply from 172.16.74.254: bytes=32 time=8ms TTL=255
Reply from 172.16.74.254: bytes=32 time<1ms TTL=255
Reply from 172.16.74.254: bytes=32 time<1ms TTL=255
Ping statistics for 172.16.74.254:
Packets: Sent = 4, Received = 4, Lost = 0 (0% loss),
Approximate round trip times in milli-seconds:
Minimum = 0ms, Maximum = 8ms, Average = 2ms
Here's what it looks like when you can't ping something:
C:\>ping 172.16.74.253
Pinging 172.16.74.253 with 32 bytes of data:
Request timed out.
Request timed out.
Request timed out.
Request timed out.
Ping statistics for 172.16.74.253:
Packets: Sent = 4, Received = 0, Lost = 4 (100% loss),
If you want to continually ping something add "-t" at the end. eg. ping 192.168.1.1 -t
To stop it, press Ctrl+C