It's never made much sense to me either.  In many stories she's seen complaining about his bad temper and leaving him, but always starts missing him and takes him back because of his underlying "sweetness".  

I think Midge is one of the most poorly developed characters.  I've never been able to work up much interest in her at all.

I guess Midge puts up with Moose's violent behavior the same way he puts up to her major unfaithfulness. I mean, we always see Reggie and Archie getting yelled at (beat up) for dating Midge, but what the heck about her?! I mean she's the one who says yes to those guys. I never understand those comics where she tells Reggie how Moose is out of town and they should be careful when going out.

Moose and Midge=Dysfunctional relationship to the max!

In the Archie comic books I grew up with, there really wasn't much of anything "good" about Moose's character.  He was the extreme stereotypical dumb jock.  And he had a violent temper.

Midge was the gorgeous "unattainable woman" - unattainable because her big ape of a boyfriend would beat up anyone who even looked at her.  But Midge, left to herself, was very attainable.  She would dump Moose, or conspire with Reggie to get him out of the way for awhile.  And she would make out with any cute guy (especially Reggie, but there were others) who came around as long as Moose wasn't nearby.  She obviously wasn't committed to Moose and even felt trapped and enslaved by him at times.

It was certainly hard to root for Moose and Midge as a couple!

There was an older story (1950's?) where Big Moose took up bird watching and was so obsessed with his new hobby that he no longer beat up other guys for talking to Midge.  Midge feels extremely slighted by this and tries to get Moose back to his old jealous self by flirting with other boys right in front of him.

A somewhat related story that appeared in a digest a while back...

Midge is softening Moose's image - "peace, love, harmony", etc. This annoys everyone else because it's ruining Moose's wrestling skills - even Jughead manages to pin him (and Betty comments that even she could pin Jughead). The gang tries everything they can think of to get Moose's attitude back - even to the point of Archie kissing Midge. However, nothing works, until Archie remembers an old quote from Rudyard Kipling saying that the female is more deadly than the male. Archie talks Veronica into kissing Moose as she has a reputation for wrapping guys around her little finger...

As soon as Midge sees this, she gets really ticked and creams Veronica. When Moose asks her "What about peace and love", etc., her reply is "Oh shut up!".

Thanks for recalling that story, Oldiesmann.  I thought I remembered a story where Midge beat up Veronica out of jealousy for Moose, but I wasn't certain.  That was a creative twist in the writing!

I think the reason Mike couldn't come up with any reasons is that there aren't any!