I don't understand why people keep referring everyone to "troubleshooting guides". Hopefully, they have done that BEFORE asking questions!
The problem you are experiencing is VERY common. I, myself, have been using ATVs for several years with no problem. Then, suddenly, it starts cutting out. My Airport Expresses also drop in and out. I assumed it was network interference or my Airport Extreme transmission power was going away. After many hour of troubleshooting it occurred to me that the AXpress started having issues AFTER a firmware update. Same was true for both of my ATVs.
Something about the current firmware is not right and Apple doesn't seem to want to address it. I assume that it has to do with different OSs but I am not a Systems Analyst. (so, what do I know)
The best advice I've gotten is to do the following:
(keep in mind, I am using OS V.10.7.5 [Lion] you may see something different if you are using another OS)
-Open "System Preferences)
-Select "Network"
-On the left you will see something called "Service Order"
-At the bottom of this window are a "+", "-" and "Gear" symbol
-Select the drop-down menu of the "gear" symbol
-Select the "Set Service Order" menu selection
-Follow the instructions to put "Wi-Fi" at the top of this list (dragging the items to where you want them on my OS)
-Apply the changes ("Apply" button)
-And, for good measure, restart your modem/router, base station, computer and ATV (as well as anything else using your Wi-Fi network) This step is probably not necessary but it is a good idea!
This suggestion/procedure was given to me by another on this forum and, so far, seems to be helping quite alot!
I hope this works for you too!!
Eric