Reserved boxes are on a different tab called 'reserved boxes' when you go to board your horse. If you reserved the box to yourself it will not appear in the public availability list so will not be searchable.

It is also possible that while you were reserving an empty box to yourself, someone else boarded a horse there or that you reserved a box for yourself that already had a horse boarded and you will have to wait until the board expires to be able to use it.

A little tip if you are making or buying more boxes that you wish to reserve to yourself, temporarily increase your boarder fees to the maximum 200e a night or add a very high skilled limit until you have the boxes reserved then reduce the skills and/or price back down. This will make it far less likely that someone else will board a horse in the minute it takes you to get it reserved for yourself.