It is possible to recoat over most powder coatings. The problems you observed earlier could be due either to contamination, or improper selection of the topcoat, or (less likely) a very unusual powder that is more difficult than usual to recoat.
Certain tool boxes may be more difficult than most articles to recoat successfully, as there have been known to be tool box manufacturers that require extreme chemical resistance when specifying their powder. (Others should be a piece of cake to recoat.) Having said that, it should be possible for you to get the job done succesfully, albeit with a little more effort than usual. Here's how I would proceed:
1. Remove the peeling topcoat completely and thoroughly.
2. Go ahead and sand the powder coating surface thoroughly. I'd use something fairly coarse, probably around 120 to 220. Finer is less advisable for what you're trying to do here.
3. Your good candidates for liquid topcoats would include either epoxy-polyamide primers, or a 2K urethane. If you should wind up sanding through the powder to bare metal in a spot or two by accident, then you might lean more in the direction of the epoxy. You should do a small test spot in an inconspicuous place to see how the adhesion is going to be on the particular product you wish to use before you paint the whole thing. This is a critical step- don't skip it! If you have multiple choices, your best chances of sucess will probably be paints with fairly strong solvents, preferably including some ketones like MIBK (methyl isobutyl ketone), MAK (methyl amyl ketone), or (MEK) methyl ethyl ketone, or esters like butyl acetate. I would definitely stay away from single component basecoats as your finish directly over the powder (some do work sucessfully, but your chances of sucess are improved with a two component product, all other things being equal).
4. Let your test spot cure thoroughly (best several days to a week at 70F or above), then take a knife and cut an X through the topcoat. Put some stong tape on it and check the adhesion. A proper choice of topcoat should be one that gives you 100% adhesion.
5. Once you've found a topcoat that works according to your test spot, proceed with coating the box.
6. In the highly unlikely event that you can't find a topcoat that gives you good adhesion on your test spot, it may be less hassel to sand the powder off entirely. However, in 30 years in the business, I've yet to see a powder coating that can't be topcoated sucessfully IF the proper steps and an optimum topcoat are used.
Good luck on your project. others on this forum might appreciate hearing how you get along and what topcoat you found to work for you.