Should a link opened/closed by a chain-breaker be stiff afterwards? I disassembled my bike's drivetrain to degrease and regrease all the components. I used a chain-breaker for the first time (previous bikes had a master link) to open a chain link and remove the chain. Afterwards, I reassembled the chain but found the link I'd opened is very stiff to the point where, as the link emerges from the chainring, it stays bent until it moves through the derailer and which point it snaps straight again.

I tried making small adjustments to the rivet holding the link together and adding additional lubricant with no success. I even removed that link from the chain completely (assuming I'd bent something slightly), only to have the next link I opened/closed become the stiff one.

Is this normal after using a chain-breaker to open a link? Should I expect the stiffness in the link to work itself out, or have I done something wrong? Is there anything else I can try to loosen up the stiff link?
Only if you didn't relieve the link after putting it back together.  It's standard procedure (if you read the instructions that came with the tool) -- you stick the chain tool into the "stiff" link so that the anvil is BETWEEN the sides of the link and only catches the near face, then crank the tool's pin down VERY SLIGHTLY against the chain pin, just enough to create some play.