Hi, and welcome to the forums.
This section is for welcoming new members, so your support request is misplaced, but I’ll try to help. In addition, you haven’t provided all the required info for a support request, but you have told me enough to suspect the cause.
Basically, using peer to peer technologies, your computer has to make a large number of tcp and udp connections to both look for peers, and transfer data to/from the peers it connects to. What appears to be happening is your router is being overwhelmed with connections and is becoming unresponsive. Most modern well designed routers have no problem running even a large number of torrents, but you may have either a poorly designed one, or one that has a known problem.
The first avenue to explore is to see if your router has a firmware update available. These are often issued to address such problems.
Buying a better device is also an option.
If you must live with the router in its current state, then there are some things you can do to lessen the impact bitcomet has on it. There are two things to look at here, the total bandwidth used, and the total number of connections used.
Limiting your bandwidth is important, but you need to know exactly how much your connection provides in reality (not advertised speeds). This can be done by shutting down everything that uses the internet on all computers and opening a single webpage at speedtest.net (or similar service). Run several speed tests on several local servers and report the results.
You will likely find your upload speed is much lower then your download, so what you need to do is find your speed in kB/s (not kb/s), then limit bitcomets “global max upload speed” to about 80% of this tested maximum. This will reserve enough upload bandwidth for communications to be timely and not interrupt all web usage. It should also greatly increase your download efficiency as well.
If your still finding your router is locking up on you, you can try limiting the total number of connections bitcomet makes, but to put it simple, a routers job is effortless if all your doing is browsing websites and doing a random direct download now and then, so the worst products made should be able to handle that, but when running torrents, your asking it to handle upto thousands of concurrent connections. This is something that any good router can do without issue, so if yours cannot, I’d seriously consider replacing it.