This issue has been encountered by several people (including myself) already. The last time as I played Arma3 on a fresh installed PC, without any active mods.
The following helped to solve the issue (as stupid as it sounds):
1) Create a new loadout (content does not matter) on one of the Ahoyworld-servers. Not sure, if this step is necessary, but I performed it anyway.
2) Open the loadout-loading screen and click onto randomly selected entries, no matter if they are greyed out or not.
3) Load some of them and repeat step 2.
The load-button should become active again for all the entries.
The other option is to recreate your Arma3-profile from scratch. This was the solution, which was provided by some external forums, but since the above described steps worked for me, I have not tried the other options.
TL got a reaction from Lindi in I&A Arsenal - not loading loadouts.