Hi both, I'm the author of HL Twitter. So far only a tiny handful of users have reported trouble with the automatic importer, and I haven't been able to find a common cause. If you could some information about your WordPress set-up (version, PHP version, host OS(linux/win), and list of plugins) it would greatly help me solve this issue once and for all.
For now, there is a built-in fallback that you can use which requires setting up a cron job. Details are on the FAQ, near the bottom: http://wordpress.org/extend/plugins/hl-twitter/faq/
Sorry for any inconvenience this might have caused you both.