Maps in Minecraft have a specific ID in the world file that is designated to it after it's generated using an empty map. When you generate maps to the 32,767th ID (or the 16 bit integer limit), creating any new map IDs after that will cause the maps to become completely disabled and unusable.

Generating any new maps past the ID 32,767 will make every map image and ID default to map ID 0. Effectively disabling the creation of new maps in the world file. This will remain an issue with any map you make until you generate another 32,767 new maps. After which, the maps will no longer default to map ID 0, but instead will begin overwriting the original 32,767 maps.

This has caused issues on several servers with players experiencing their maps not only disappearing, but also being completely disabled for months. This can be caused by someone intentionally going past the 32,767 limit, or the server having a large enough player base creating lots of maps. While it may be very unlikely, the issue may have also occurred in long running single player worlds as well.

With this bug in place, the player is limited with the amount of maps they can create, a whole game play mechanic could be completely ripped from them, they could have all of their maps disappear, and the issue is only going to proceed to get worse as more maps are created on servers and SP worlds with long lasting worlds.

Given the effects this bug could have, I would request that this issue is not treated as a suggestion that the "map limit needs to be increased". I would prefer it be looked at as an internal flaw with the game that has and is breaking a well loved mechanic. More or less, it's an core issue with the game and it should be treated like what it is, a bug.

Here is a great reference video outlining the problem, what causes it, possible and reasonable solutions, and all of the details relating to this issue.
https://www.youtube.com/watch?v=Ec_c5FqRByw