I upgraded yesterday to Version 18.104.22.168 without any such problems! All working perfectly.
But if you do want to revert to an earlier version, you would be best un-installing your latest version before installing the older one. I believe you will still have your Contacts in place when you re-install.
BTW - I upgraded my Skype of my own accord, I was not prompted to do so - because of this, I am wondering if there is a rogue bit of nastiness out there causing your problem. Might be a good idea to run all your anti-everything programs before doing your re-install of Skype. Just a thought!
Having posted earlier about v3.8 (Pepper9)and reading more comments I decided to give version 22.214.171.124 a try and did as Technotiger did - upgraded on my own accord from within the SKYPE menu. Downloaded no problem and had an hour conference call to Canada, Wiltshire and home last night with no problems. Quality of sound was excellent according to my friends in Canada, better than when using 3.8. Picture seemed OK when I was calling my friend in Wiltshire before going over to conference call. Hope it continues!!