In this game:

http://www.wargear.net/games/player/15852

I eliminated a player and took his cards.  I have a set I can play (3 Loves) but I can't click on them to trade them in.

You can only trade mid-turn if:

A. The map allows return to placement from attack, or
B. You would have more than 5 cards in your hand at the end of the turn if you didn't trade in.

My guess is that for the game you've posted, neither applies.

Then why is it bringing up a "Trade cards" message? That is just misleading.

Kjeld wrote:
B. You would have more than 5 cards in your hand at the end of the turn if you didn't trade in.

Just to clarify, it's if you have greater than or equal to the max number of cards allowed, on that board it's set to 6, so if you have 6 or more cards due to an elimination you should be forced to turn in mid-turn.

Seems odd that the Trade Card window is popping up but you can't trade, I do think there is something funky with the Trade Card window as I think I've notice some unclear behavior with it before but not enough to know how to reproduce or see with a simple flow.

C. There is also an elimination bonus AND it exceeds the maximum reserve armies allowed for that board.

(in effect this forces a Return to Placement)