The problem usually happens because your router can't handle too many connections at once.
Bit torrent programs like uTorrent open many connections at once to get total high speed in transfers.
Every router has its own limits to the maximum connections it can handle.
(Many routers can handle up to 255 connections only and even less than that)
To fine tune your bittorrent or emule or whatever P2P program you use to the maximum allowed, i suggest to do the following :
Set your P2P client to a very low amount of max connections in the settings.
I will demonstrate using uTorrent settings:
open options-> preferences , and then click 'bandwidth', you should see something like this:
start by setting both values to 25 and then download some popular file (just one).
Have a look at the total amount of connections you get by adding these 2 values:
(in the example above it is 120+55=177, where i set the max to 200, the remaining 23 connections can be uploads- which you should limit too - or connections being made at this moment)
now wait a few minutes see the connection is stable and then add 25 more to both settings above (while the download still continues) and re-check your connection download stability by waiting a few more minutes.
once you get a disconnections go back to the previous setting you had (if it disconnects at 200, then set it back to 175).
I found that my router, tplink WR641/2, can probably handle around the 200 connections.
Remember you have other connections in the house, including other computers/cellphones on the same router and the same computer browsing the web... so leave enough for everything.
Hope I helped !