(EDIT - in the post below I am suspecting that it is the "under cover" under the engine as those are known to come loose after an oil change if the screws are not reinstalled correctly. However I'm now realizing that you said it seems to be under the driver's seat, so it may be something else.)
It sounds like it may be the "under cover" which is a thin metal pan underneath the engine. It is removed whenever the oil and filter is changed to gain access to them. Did you recently have your oil changed somewhere? The cover is attached with eight screws, they aren't screws in the normal sense as they don't have threads, you use a slotted screwdriver to turn them 90 degrees counter-clockwise to remove the screw, and 90 degrees clockwise to tighten. After removing all of the screws the cover drops off, but not immediately as there are also a couple of flanges that hold the cover loosely in place, so after the screws are removed you slide the cover backwards (if I remember correctly) about a half an inch and then the cover drops off.
At least one person reported that after having their oil changed the shop failed to put the screws back in. It might hold on for a while with just the flanges but then fall off. In your case maybe they didn't put all of the screws in correctly and over time they started to loosen.
The screws are relatively inexpensive to replace, the cover is not, mainly because it is sold only as part of a larger assembly.
If it does turn out to be the under cover and some screws are missing, probably the best thing to do is remove the remaining screws (a coin should work if you don't have a screwdriver) and then remove the pan and just keep it in the trunk until you get home. The cover seems to be there mainly for airflow although it probably also provides some protection from damage if you run over something, but just for the ride home you should be okay. Then you can see if the cover can be salvaged with what's left instead of having to replace it.
