Getting the TIme Capsule to work reliably in the network when it is not the main router can be difficult. There are a lot of posts complaining about dropouts like yours.
There are a couple of important things you can do to help it.. apart from what Tesserax suggested.
The key one is giving the TC a static IP.
Bonjour does not work very well with lots of different routers.
What is make and model of your main router?
So Time Capsules are yesterday's technology
Certainly Apple have given up making routers. And the Gen5 which was released to replace the Gen4 A1409 you own was never upgraded over its entire lifetime .. you won't find many routers on sale for 6 years.. and ones that are get hardware updates. Better processors.. shielding for USB3 which turned out to be a problem. And continual advancement in functionality.. eg mesh. A good example is the Asus RT-AC68U which has also been on sale for as long as the Gen5 TC.
Apple improved security and did bug fixes but never improved the hardware (like upgrading USB2 to USB3, which is easy) or added functionality like SMB2 & 3 which could really stretch their life.
But I personally like the A1409. I still have a couple of them working and have continued to repair them. They are the easy to work on and solidly made. The next version A1470 is a real mess inside.
To be practical unless you are a DIYer who likes repairing stuff it is time to replace the TC.
I don't think you really need a replacement since your backup strategy is comprehensive.
What brand is the NAS you are using?
What backup strategy might you recommend?
Create a bootable clone on USB drive. It sounds like you are doing something like it with Carbonite. I use Carbon Copy Cloner.
Time Machine is great when it works but has become very flakey in more recent Mac OS. It regularly wipes out its own backup so we see regular complaints based on this message.
I take it you don't care much for NAS storage ... ?
We use Synology NAS and recommend them.
If people want network backups then Apple offers nothing except using another computer since High Sierra.
See https://www.howtogeek.com/330288/how-to-set-up-your-mac-to-act-as-a-networked-time-machine-drive/
I do continue to run Time Machine to a backup.. either a TC of various descriptions or USB drive on computer so local backup or another router like Asus or Synology which support Time Machine to USB 3 drive.