The Time Capsule is telling you that you do not have it configured correctly to work most effectively on your network.
Double NAT is usually an indication that you another router "upstream" from the Time Capsule....(you might call this device your "modem", but it is likely a router). This can cause network slow downs and IP address conflicts.
Both your "modem" and the Time Capsule are trying to perform routing duties. You only want one device on a network to handle the routing chores.
If you want to pursue this further, what is the make and model number of your "modem"?
Not sure what the model is... I've been using this modem for about 7 months and the TC since about 2008 (I believe). Haven't had any issues up until recently. I did notice that I can get back online if I ONLY reset the TC versus resetting the modem and TC - if I do it that way, it still blinks amber.
Anyway, I can check that later. Thanks.