Why does the mirror modifier disappear when I merge objects together? For starters, I started studying blender it's been just a couple of weeks.

So, just for fun, I started modeling a key using a torus, a cylinder and a cube, as you can probably figure out by the images below:







It was all fun and games 'till I tried to merge the objects into one using Ctrl+J, weirdly the result was this:



I've tried changing the sequence of selection when I was merging, but it didn't solve the problem. That little thingy still disappeared. I think this error is due to the mirror modifier I used on the last piece of the key, and maybe when I merged it something wasn't compatible.

I also tried adding the same modifier to the other pieces but the result was the same. The last piece in detail can be seen in the link with the screenshots.

If anyone would kindly explain what's going on and hopefully come up with a solution I would be very much appreciated.
When you merge two or more objects together, all selected objects will inherit the modifier stack of the active object (the object selected last).
If you're selecting the teeth object first (the object that has the Mirror modifier) then the key object (the active object that doesn't have it), the Mirror modifier will be deleted, since the active object doesn't have one.
The best solution is to copy the object that has the Mirror modifier, put it on a different layer for backup, then go to the original object and apply the Mirror modifier before merging it with the key object.