In the last week or so, NS has been disconnecting for no reason from games. My latency can be a 14 or up to 50 depending on server, and it will stop, and the "Warning: Connection Problems" in bold red will show up. I can still be connected to irc, ventrillo, whatever, and no problems come up in those programs. Any help would be appreciated.
I access the internet through a router on a DSL connection.

That sounds like it would be a server problem, perhaps the server crashing, or lagging. Try other servers if you haven't done so yet. You could also try the following commands in console:

rate 20000
fps_max 101
net_graph 3 <- with net_graph 3 it allowes you to view your connection to the server to put it simply; it shows your loss, etc.

Oh yes, I have tried different servers. They all seem to be doing it.

Also, I was watching it, and whenever I am in game, I have an in of about 70 and an out of 40 and no loss or choke, but whenever this problem happens, and I disconnect from a game it goes to 3.14 in, and the same out...

rate 20000
fps_max 101
fps_modem 101
cl_cmdrate 101
cl_updaterate 101
net_graph 3

If you have loss or choke lower cl_cmdrate and cl_updaterate until it dissappears.