One of the first things that Apple will do when you call them is ask you to perform a factory default reset on the Time Capsule and then set it up again. You might want to give that a try before you call support if only to save some time on the phone. Sometimes a complete reset will do the trick, sometimes not. It is probably worth a try.
To perform a factory default reset......
Power off the Time Capsule by pulling the power cord from the back of the device. Be sure that the TC is not backing up at the time.
Wait a minute
Hold in the reset button first, and keep holding it in for an additional 7-8 seconds while you simultaneously plug the power back into the Time Capsule. (This is tricky....you almost need to have 3 hands to do this)
Release the reset button after the hold period and allow a full minute for the Time Capsule to restart to a slow, blinking amber light status
The Time Capsule is now fully reset and can be set up again. The default reset will not affect the data on the Time Capsule hard drive in any way.
If the problems persist, then there are a few more checks that you can perform.....or.....if you prefer, you can do these before you try a factory default reset on the Time Capsule.
If you can do without wireless for a few days, try connecting a computer directly to one of the LAN <--> ports on the Time Capsule to see if the connection is maintained. If it is, you likely have a wireless radio problem on the Time Capsule. In that case, you can still use the Time Capsule as a wired hard drive and simply turn off the wireless and use another router for wireless.
If the connection drops when the computer is connected to the Ethernet port, then that points to a power supply issue on the Time Capsule. On average, the TC power supply starts heading downhill at about 3 years of age, and when this occurs, connection drops begin. The drops will increase in frequency as time passes. It's probably time for a replacement.