This was a concern for me when I started researching TVs early last year. It seems to me that the main culprit in this trend is the delay introduced by video processing in modern LCD TVs. The video can take substantially longer to display and, if there's no way to delay the audio, you end up with audio sync issues.
I decided that it made sense to get a new HDMI AVR (there were other reasons I needed one). It turns out that I may not have had problems after all because I ended up buying a DLP RPTV, but I've been very happy with my new Denon 1909.
If it's at all feasible, I would suggest that upgrading to an HDMI-capable AVR is the way to go. I got my Denon from J&R for a great price, but the Yamaha 663 (?) and the Onkyo 606 (?) can be had for a very reasonable price. The auto-sync feature is one of many reasons to consider an upgrade.