When I flush my toilet, the bowl empties as usual and fills as usual, but the water level in the bowl begins to slowly drain and maintains a lower lever than normal. I don't know what is causing this or how to correct the situation. This has been going on for approximately a week. I have checked the basement and don't find any leaks in the drain pipe. I don't know what else to check. Can you tell me where my problem is and how to fix it? The toilet does still work, but the water level in the bowl does not stay as high as it used to.

The trap in a commode is like a bowl and if you pour water in the bowl it will fill up to the rim of the bowl any water you add after that will spill over the rim of the bowl but if you quit adding water it will empty to the rim and no more will spill out. That is exactly how the trap works and once the trap has reached the water level it should remain at that level. There are two things that would make the level go down, one is for the trap to have a hole or a crack in it but you say you don't see any water on the floor. There are some commodes that are made in such a way that if you had a crack or a hole in the trap the water would leak down to that level and stop and the water that has leaked out of the hole or crack just goes down the sewer because of the way the commode is made.
The second thing that could make the water go down is an action called osmosis, think back to the bowl and think what would happen if you put a heavy string over the rim of the bowl, some of the string down in the water and some of the string hanging over the rim and on the outside of the bowl. The water would soak into the string and eventually move up the string till it started dripping off the string that is outside of the bowl. This action would stop when the string in the bowl became higher than the water level in the bowl.
This same thing can happen if a heavy wad of paper or something is hung up in the trap and acting like the string.

How can I increase the water level in the toilet bowl?

Increasing the level won't help much, read-on ! There could also be a factory defect in the bowl. Sometimes in casting the bowl there is a small bubble in the china. Instead of junking the bowl the manufacture will put a porcelain patch over the hole and send it on through. On occasion the patch will fail allowing the water to seep out of the bowl. If that's the case you would have a full bowl after you flushed and the bowl filled but some time later you would notice a drop in the bowl level. The only other thing might be if you dropped something in the bowl and cracked it. If you're worried about where the water's going, in both cases it drains back down into the sewer and not under the bowl on the floor.
Sometimes a blocked vent can "vacume" water out of a bowl. Does the level "bounce" up and down? Regards, Tom