Sorry.. not making the capx to test this myself, but this should work.
Firstly.. lets assume that you are using the regular platform system for movement. Secondly.. that we are talking something that is only one-direction (running from left to right) and the user don't have ability to jump&etc while inside a loop.
At the bottom of the loop, add invisible sprite that is hit by player running left to right.
Once the hit happens. Store the player X and Y speed, position etc.
Disable the platform-behaviour..+ calculate the angular speed (based on loop radius) and
While inside the loop: keep moving player forward (get x/y coordinates from angle) increasing the angle so that momentum appears to be kept.
When the player is once again at the bottom of the loop. (where the loop started)
Kill the angular-move loop, reset the player coordinates (in case of rounding errors) and enable the platform behavior so that player can continue running towards the right.