Can you reroll a die you just rerolled (with another effect)?

No.

Rule: "Reroll" RRG, Page 22 (Which immediately references "Attack Step 3: RRG, Page 5):

Each die may be rerolled only once per attack regardless of who is rerolling the die.

And if rerolling a Skill check?

And if rerolling a Skill check?

I'd say the same: no reroll of a rerolled dice

I do not think there is much out there that allow for a re-roll of a skill check, let alone the possibility of a re-re-reroll to even become an viable situation, but if it is out there, I would also agree with Forensicus. No rerolling of a rerolled die.

There are some:

Force Adep
Smuggler's Luck
Slicing Tools
Combat Visor
Survival Gear