What difference would it make to the viability of automatic reconnect, if you were asked for the password again on reconnect?
i.e. when the connection to the machine drops (reboot, network outage etc), the client software will periodically probe the machine to check whether it's responding on TCP port 4899 (or whichever you've chosen), but will then simply display an in-window password prompt . Basically think of the MS RDP client, but allow for a longer maximum retry timeout.
This way, no password need be memorised, but with slow reboots and network outages I don't have to sit there trying over and over and over to get back onto the machine: the window will flash once the connection is restored. This will save a lot of frustration! All I need to do is put the password back in to complete the reconnect.
 I say this because Radmin Viewer incorrectly forces focus on dialog boxes, so anything that reconnects in the background will bring itself frontmost and steal focus. However, this is a fundamental flaw that should really be addressed across the board: display a dialog without raising it to the top of the window stack. If the program is in the background, it should flash for attention.
That's great news. Obviously I dearly hope that it will be achieved without involving a focus change. I notice when I have RDP sessions running in the background that the reconnect will always steal focus. Even if it doesn't bring the window frontmost (which is attempts), I'll be typing and suddenly find that no more letters are appearing because some minimised or buried RDP window has stolen the focus from whatever I was doing.
I really hope that this doesn't happen with Radmin – I expect it to flash its taskbar button if it really needs my attention!
Also, under XP and earlier you can also change and animate the taskbar button icon, which very few people are aware of -- FlashFXP is the only program I can think of that makes use of this feature. Sadly in Windows 7 it's not all that useful as multiple windows now share a single button and therefore a single icon.