The following is with regards to Unburden.
The description of Unburden (
http://www.smogon.com/bw/abilities/unburden) says that "Regaining an item does not remove the boost.", but I had an experience to the contrary.
I had a Bronzong (Sassy, Leftovers, 252 HP/4 Def/252 SpDef, 0 Speed IVs) in on an Unburden Hitmonlee. He used up his Normal Gem with Fake Out, thus doubling his Speed. I went for Gyro Ball, which should be 150 base power (25 * (600/63) ~ 238 > 150), but he used Thief first, stealing my Leftovers and then living the Gyro Ball with ~15%. If Unburden was not lost upon regaining an item, the hit should've done 100.4% - 118.2%, guaranteed OHKO. However, without the Unburden boost and thus only 300 Speed, it would only do 80.6% - 94.6% (120 base power).
To check this, I went on Pokemon Online and tested my hypothesis. I used a standard offensive Shaymin vs Hitmonlee. Shaymin outsped on the first turn, and Hitmonlee activated Unburden (via Gem usage). Hitmonlee then outsped Shaymin and used Thief to steal my item. On turn 3, Shaymin was once again faster than Hitmonlee with his newly acquired item.
So in conclusion, the Unburden boost IS lost upon gaining a new item (at least in Gen5, this may not be true for Gen4).
For those interested in seeing the scenario I described, look at
http://www.youtube.com/watch?v=QZ5d5jSUe0I at 2:19. If you want to test the PO situation, it's simple enough to do.