Let's assume such a sequence exists, and fix a working sequence. Clearly, this sequence does not contain an equal number of NORTH and SOUTH directions, otherwise the robot would return to the starting cell in an infinite 1-wide north-south corridor. The same goes for WESTs and EASTs.
Without loss of generality, we can assume there are more NORTHs than SOUTHs and more EASTs than WESTs. Now let's build a maze to test the sequence. Start with the empty plane. First, we are going to build a straight infinite wall stretching from east to west. The latitude of this wall will be important. If there are $a$ NORTH and $b$ SOUTH directions in the sequence, we want this wall to block exactly $(a-b)$ NORTH directions. This can be done by referring to the following statement:
If an infinite south-facing wall that is $y$ cells north from the starting cell absorbs $n$ NORTHs from the sequence, then an infinite south-facing wall $y+1$ cells north from the starting point will block at least $(n-1)$ NORTHs. This is true because once the robot has bumped into the wall for the first time, it is now in front of the wall, and the rest of the sequence will be executed the same way as if the wall were pushed 1 more cell to the north.
An infinite wall directly on the north edge of the starting cell will obviously block at least $(a-b)$ NORTHs. If it blocks more than that, move the wall 1 cell to the north. If it still does, move it 1 cell further again. At some point it will block exactly $(a-b)$ NORTH directions. That will be the final place of this wall.
Then with the same method we build an infinite west-facing wall to annihilate any east-west movement.
The sequence will return to the starting point in this 'maze'. This contradiction shows that there is no sequence capable of making progress in every infinite maze.
As @NeilW pointed out, once we put our south-facing wall in its place, we can completely ignore horizontal movement by building infinite vertical walls on the left and right edge of the starting cell. Of course, they don't even need to be infinite. They just have to be longer than the sequence itself.