Recording sound from specific applications is a very cool feature, but since my PCs have Windows Vista or Windows 7, I can't use it.
I haven't been recording Windows Media and Real Player streams recently. There are plenty of users using
Replay AV for recording radio, so I suggest you to ask them whether Replay AV can reconnect reliably or not.
Personally I really liked downloading/capturing Windows Media and Real Media/Real Audio streams with
WM Recorder. And the latest version works fine with HTTP and RTMP flash player streams.
Both
WM Recorder and
Replay AV have free trials, but I don't think the trial versions will be enough for your tests. But both products have a 30-day unconditional money-back guarantee.
You may also try to download your streams using shareware
NetTransport and freeware
Orbit Downloader.
Or you may use multiple programs. For downloading Windows Media streams you may try freeware
GetASFStream,
SDPReceiver.
StreamboxVCR should still work fine for real streams.