Essentially this can be because of several reasons.
1) Router DHCP Lease Time is set to 1 hour.
2) Modem DHCP Lease Time is set to 1 hour.
3) Router Hardware is flaky and auto-reboots itself every hour (maybe a built-in firewall is generating log files and runs out of temp storage so needs to reboot itself, or some other reason)
4) Modem Hardware is flaky and failsafes to an auto reboot.
5) Other reasons (Windows, Playstation firmware, wifi network interference, etc) could also create an hourly disconnect

Since there are so many possible avenues of what could be wrong, it's usually best to try and eliminate as many possible reasons first then look into them to confirm if that's the reason why.

So the first question is: What kind of internet do you have? DSL Internet? Cable Internet? Other?

Second Question (assuming you have Cable Internet)*:
Are your router and modem separate devices?
(Is there any chance that your modem is a modem+router combo but just HAPPENS to be connected to a router?)

IF you definitely do have a separate router and a separate modem, try connecting directly to the modem with a Ethernet cable.

If you STILL have the problem every hour while directly connected, then this is something your internet service provider can look into for you. (Just tell them your internet cuts out every hour, don't mention the game because they'll just play blame game with you and say it's their fault) -- essentially this IS most likely their fault OR mayyyybeee something up with your computer/Playstation -- but that's a bit less likely.

If you're NOT having the issue with it directly connected, then chances are that your router is having issues, and the simplest solution may very well by to buy a new router (or have someone help you fix the configuration on it).

*Note: The direct modem->device connection only works with Cable Modems, DSL modems are more complicated.

Sorry my reply isn't simple, but sadly the problem could be so many things that it's hard to provide a simple answer.