Like I tried to say in the initial problem statement: it's intermittent and primarily seen with Thunderbird. (I see from stats that you used Firefox 2.0.0, and no one has reported a problem with that.) feedvalidator comments indicate that some RSS readers may strip whitespace at the top of an RSS feed (Firefox could be one that does). So you may have encountered the whitespace and still not have encountered the "invalid feed" error.
What I'm really looking for is a methodology to troubleshoot why the RSS feed varies over time: what you called "the common factor".
I tried restarting Apache to see if it's related to the initial run of some code - no luck. I disabled cache to see if that behaves differently - no luck. I pruned blank lines out of some home grown plugins (and checked the others for blank lines) - no luck.
I use wp-cache plugin, which appears to cache RSS feed as well as other pages. Unless I'm mistaken, sometimes the cached results include spurious whitespace and sometimes not. That baffles me completely.
I tried switching cache off (and clearing the cache) but couldn't determine a pattern. The problem behavior is too rare to see a pattern yet.
Any suggestions about what to ask the user or what "wires to jiggle" to try to reproduce and isolate this behavior? Thanks in advance.
Anyone ever seen "invalid RSS feed" from Thunderbird on another WordPress site?