Perhaps a confusing question, but did you mean 3000 kbps or 3000 KB/s? There's a major difference. kbps = kilo bits per second. KB/s = Kilo Bytes per second. 8 bits = 1 Byte. Sizes on your computer are normally shown in Bytes or KiloBytes (KB), etc. Normally LW shows speeds in KiloBytes (KB/s). Some other p2p programs show speeds in kilobits per second. (Browser speed test sites usually show speeds in kbps not KB/s).

Arguably, downloading at 3000 KB/s (3 MB/s) should = 180000 KB (180 MB) per minute

With speeds suddenly dropping soon after starting, gives impression of ISP bandwidth shaping. However, in your scenario it only happens for one account & the program itself is freezing up on you. So that suggests the problem is at your end.

Yes, I suspect you have your finger on the spot with number of connections your set up can handle. Your router was an earlier thought of mine also. This problem issue is common for wireless setups. And especially if torrents are involved because torrents will often make many more connections & be constantly messaging to and from the tracker server & each of the other peers in the same swarm.

Can you tell us the brand and model of your router and any other connection equipment you are using?
Is it a wireless router?