Sounds strange. Can you be absolutely sure that the Uji Countdown plugin is the source of the problem?
I ask because I have recently activated Uji Countdown on a fresh install of WP 3.8.1 and it works perfectly fine. I have no issues to report of whatsoever. On the other hand, it being a fresh install of WP it’s not exactly a complex site packed with features and content so of course there is currently minimal risk of conflict with other stuff on the site, but my point still stands: Can you be absolutely sure that the Uji Countdown plugin was the actual source of the problems you experienced?
Mind you, I’m using the Premium Plus version ($26) and I can’t say if that makes a difference in one way or another.
However, to me Uji Countdown (Premium Plus) is the best (and most beautiful) countdown plugin I’ve tried to date – and I’ve tried a lot.