I can't find any hard evidence that Mediacom are blocking/throttling p2p at certain times of day, but this thread suggests it
[RANT] Mediacom blocking P2P traffic - Dont waste your money - dslreports.com

There have been a few Mediacom users lately who've been having problems! Maybe this is happening during peak times?
See if you can connect later in the day or at night, around the same time that you downloaded Pro & could connect.

See whether changing ports helps. In LW tools > options > advanced > firewall config. Change LW's listening port to 64049 (or something in the range of 49152 - 65535) > apply > ok.

Some people have had connection problems with that latest Java update, if you like you can try this version instead. Download the JRE offline installer & remove any other Java versions before you install this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

If you let us know the brand & model number of your modem/router, we might be able to help with the firewall issue