https://i.imgur.com/yJzlKD4.png
I can use the repair pack to fix the chute that's outputting items from the chest, but the inputting one can't be fixed. Picking it up puts a fully-fixed chute in my inventory.
This only seems to be happening to chutes which were placed as outputting chutes, but were turned around by placing a belt moving towards the chest. If you place the chest and belt first, then add the chute, it is immediately placed as an input chute and can be repaired if damaged.