Thanks to Robert's input, this problem has now been solved. A combination of conditions was causing AbsoluteTelnet to enter a state that could not be fixed without exiting and re-starting the application. Side effects included improper alignment of command line, improper display of vi and sometimes the reduction of the screen to a single scroll line.
The problem stems from AbsoluteTelnet making an improper response to a probe from the host designed to determine the screen size. The host then does not know the true dimensions of the screen and many screen-oriented programs begin to display badly.
This problem has apparently been around for some time. The combination of events required to trigger it made it difficult to reproduce and impossible to fix. Thanks to Robert, the cause has been identified and eliminated!!
You can download the beta here:
http://www.celestialsoftware.net/telnet/AbsoluteTelnetBeta.exe
If you haven't joined the beta group yet, you can do so here:
http://www.celestialsoftware.net/telnet/beta_software.html