Suppose you wanted to actually fail your combat check and lose the fight on purpose, can you just declare that you are doing so and not make your combat rolls? In essence, letting the monster get free hits on you?

I can think of 2 situations where this would actually be favorable to the player, and there are probably more...

1. Fighting a Nightgaunt. Losing a fight to it means it sends you to the closest gate, or out of the Other World to the gate you came in on if you're in an OW. Maybe there is another tough creature you don't want to fight, or risk evading, between you and the closest gate, and losing to the Nightgaunt would get you there without risking loss of sanity or stamina. Or in an Other World you draw a Nightgaunt as an encounter in the first space, and losing to it would let you skip the next space and send you straight back to Arkham, while also getting you an explored marker.

2. You are in a location or street far away from St. Mary's Hospital, and it is critical that you get to that area of the board quickly. Losing a fight to a monster would send you straight to the Hospital, giving you a quick jump all the way across the board. If you've got the cash to get a full heal, even less of a hardship. You have basically teleported to the Hospital without having to face whatever would have come your way in the many turns it would have taken to get down there in the normal way.

So is voluntarily losing a fight a legal option, and sound like a legit strategy in the above cases?

Nope. If you have dice, gotta roll them. What you can do is move your sliders in anticipation of a NG already on the board and choose NOT to use any weapons.

Got it, thanks for the quick answer, Dam.

You'd think that if an investigator wanted to submit to being taken away by a NightGaunt, he could!

But then again, I guess this isn't an RPG and I suppose investigators would always fight whatever monstrous horror they were faced with...

This would remove one of the abilities of Nodens. Who lets you let night gaunts carry you into the gates

I tend to try to evade monsters while having a low sneak value in that cases mentioned. They do their combat damage and I'm fine.