##Focus on the positive
Focus on the positive
Board games often have many dimensions and someone may be ahead in one (or a few) dimensions, while being behind in others. For example, you may have a lot of "points", which may be how the game is ultimately scored, but she has plenty of "resources", which can be used to gain "points" in the long term (trying to keep the example general).
If she complains, you can highlight one part of the game which is going well for her.
This could (a) distract her from complaining or thinking about the big picture by giving her something to focus on, (b) get her to think of the other dimensions of the game and (c) point her towards a strategy that might help her win.
Her: There is no sense in playing, it's over anyways.
You: Well, I'm going to get a hard time winning against that giant army of yours.
OR
You: With all those mines you'll probably catch up in no time.
OR
You: I'll have a hard time winning if you manage to promote that pawn of yours.
##Don't directly disagree with her or invalidate her feelings
Don't directly disagree with her or invalidate her feelings
If she says "it's over", don't say "it's not over" nor "don't say that".
That's more confrontational and is thus more likely to make her defensive and less open to changing her mind.
##Keep it light-hearted
Keep it light-hearted
This one may or may not work, depending on her personality and your delivery, but you could try some light-hearted humour in response to what she says.
You could also combine this with focusing on the positive.
Her: There is no sense in playing, it's over anyways.
You: You're just trying to get me to let my guard down to buy you some time to finish that barracks of yours, aren't you?
##Remind her of when she caught up
Remind her of when she caught up
If you can highlight a specific time when she was behind and managed to catch up and win, that could help her believe there's still a chance she can win.
Specifics about the game would help, to make it easier to compare, but don't worry too much if you can't get it 100% right (or if you get it largely wrong, for that matter).
Her: There is no sense in playing, it's over anyways.
You: It's only 10-5. Didn't you manage to win from 10-4 last week?