"lights go out" - can you be a little more specific: which lights? All? Or, just the ones you mention? Might be a silly question, but it's pertinent.
If it's just system/transmit/receive and/or LAN light:
1. Go to http://192.168.0.1/limited.html#!/state_code/state_code_monitor and tell us the Last Error State Code. There might be a long list of those, but really just interested in that one. You might want to take a screen shot and post it here, just remember to edit out part of the image with the SAN/DSS code on it - you don't want that made publicly available.
2. Might also want to go to http://192.168.0.1/index.html#!/home/status#%2F and take a screen shot, taking care to likewise edit out the SAN/DSS code for your own protection.
3. When does this typically happen? When it is raining, heavily clouded, windy? Otherwise, what kind of weather are your experiencing?
4. Are there any kinds of foliage within 40 degrees in any direction around the dish? Any branches possibly hanging in front or to the side?
5. What about where it seems to be aimed? Is it shooting through some trees? Has someone possibly built a structure that could be blocking your signal?
6. Where exactly is the dish mounted? Is it on a pole or on your roof?
Some other things to check that are mostly power-related but may be relevant:
1. Is the power plug firmly seated in the back of the modem or is it loose? Same for the cord on the power brick.
2. Is the power cord plugged directly into a wall socket? Or are you using a power strip or UPS? If you are using a power strip or UPS, try going directly to the wall. Those devices may be limiting the power to the modem (which also powers the transceiver at the dish) to below acceptible levels.
3. Is the cable's F-connector firmly connected in the back of the modem, and (if done this way) is the other end of the cable firmly connected where it's mounted at the wall? Both should be fairly finger tight and not feel loose or 'stripped' when you touch it. If it's phyiscially possible, you might also try to to inspect the cable at the dish's transceiver.