Ditch more out of your inventory at your bank and try again? I honestly think that if your reward is say, 5 items and you only have 5 open slots in your inventory, you will not receive the reward. You MUST have one more slot open above and beyond what you need or the reward will not drop into your inventory.
There is a limit and frankly I honestly don't remember what it is, I think around like 200 max... Anywho, you can get all the info you're looking for by going to the Duty Officer screen, I think it's in the lower left hand corner of that screen, such as 172 officers of 200 or something like that.
So I have tons of space in my inventory and 26 duty officer spaces and the rewards add up to 10 duty officers.
So why can't I claim them?
Are you sure about the 26 open places ? Prisoners and Passengers DO count towards the maximum of 100. I had the same happening to me a few times. I just threw out some colonists to make space for the new ones.