I have an SAT implementation that basically works, and the fact that it works is what's giving me a few headaches. Basically there are some situations where using the SAT doesn't quite give me my intended result. One of these involves movement across multiple collision objects. Or to put it another way, if I have several collision boxes lined up next to each other such as to create something like a wall or a floor, movement along that surface while constantly applying force into that surface sometimes causes hangups, i.e. the player stops moving.

This illustration shows what I mean:

The 2 boxes on the bottom represent a floor, and the box on top/in the middle represents what my player is doing. There are several squares lined up as world obstacles to create some kind of wall, and if I move to the left across this surface while holding the down key then the issue arises. It only happens at the exact dividing point between two blocks. It only happens when moving to the left. At any rate I think I know why it happens, but I don't know how to solve it.

Basically when I update my player movement I consider which directions are pressed, naturally, so if down is pressed I will add the speed to the Y component, and so on. But due to the way my SAT is implemented, when the penetration into the shape is the same from both sides it just goes with the smallest axis that it finds first, and it checks collisions against objects in the order that they were created because it goes through a foreach loop on the list of collidable objects. So this all adds up to the effect of if I'm moving to the left over a series of boxes while holding down, it will resolve me back to the right out of the first box and then up out of the box to the right of it, and this continues as long as the penetration is the same. The odd part is that this doesn't happen every time, which I am going to attribute to some oddity regarding multiplying velocity by the game time and causing some minor discrepancies between the lengths.

Ultimately what this boils down to is that it will keep resolving me to the right and up, but this is technically expected behavior. All the solutions I can think of only address the symptoms of this problem and not the actual cause, such as not using many blocks to create walls or shapes, which is an option I'd like to keep open. I could also change which axis my algorithm defaults to, but that would just cause problems when going up/down along the walls.

What can I do to fix this?