This is a bit of a vague question but it appears that IE does send different UA strings when compatibility mode is enabled and EE (or rather CodeIgniter) does invalidate sessions by default if the user agent changes.
I've never tried this but by the look of it you can change this behaviour by editing this setting in system/expressionengine/config/session.php:
$config['sess_match_useragent'] = TRUE;
As for whether you should change this, it seems unlikely that people are switching compatibility view on and off mid-session with any frequency, but if it's something that is regularly impacting an important user then maybe there is an argument for changing it, particularly if you've already done quite a bit of debugging and there's no simple way of stopping their UA from changing all the time. It does seem like a bit of an odd problem to have though - solving that would probably be preferential.