Hello - I came across this issue last night. Twitter had some kind of outage last night (or at least something was going on as I couldn't access my timeline via my phone app).
During this period output from RSTFW and another plugin I use (pods cms) was failing to show up (and page loading on pages where the widget should appear was very slow). I did not test to see if any other plugins were not working.
I disabled RSTFW and everything was fine again. This morning with Twitter updating on my phone OK I reactivated it and everything was fine again.
Perhaps some sort of feature needs to be added that allows the plugin to work even when Twitter is down - if this is what caused the issue (i.e. still list old tweets but not to crash if it can't get new ones)
Otherwise I really like this plugin - very simple and straightforward.