If anyone's interested, I figured out what was wrong, sort of.
I don't know why, but sometimes when I click the Post button to put something up for sale it just doesn't work. It's not a matter of how many transactions I already have going. I click the Post button, I clearly see that it was clicked, yet nothing happens. I've found three solutions or workarounds that clear it up and get it working again:
1. Click the Reset button in the upper portion of the /ah window. Pretty sure that's just supposed to reset your search criteria but regardless, clicking it usually lets post things again when the button stops working.
2. Take the item I'm trying to post back into my inventory, then drag it to the /ah and try posting it again.
3. Just. Keep. Clicking. Post. Spamming the button works too.
Again, not sure why click Post doesn't work sometimes. My first thought was that it was just lag, but if that were the case wouldn't the game eventually catch up and post my item for sale? I've also not been experiencing any other symptoms of lag when this happens, so. . . ¯\_(ツ)_/¯