When my king died, the next king (oldest son) could only raise like half the army (levies) I could before. What happened?
I think the reason your levy decreased is due to your heir's vassal-leige relationship score being different than your original king's. It could also be that your levy base providing buildings are not in your heir's personal demense.
The levy system is actually kinda complex but once you have a feel for it I suspect it'll make sense.
I originally said (in comments) that I thought this was related to titles, and it's not quite right. There's a few things at play.
If you don't give your sons any land then you can end up with the "unlanded sons prestige penalty". You need to give your first son some lands (but not the 2nd or 3rd as it'll increase a chance of war on inheritance). This shouldn't affect your levy though, except as it may indirectly affect your relationship with your vassals.
I came across a pretty decent description of the levy system [here].1
If you lose any of the following, you'll see a bad drop:
Here's where you could be losing levy... especially note that if the castle isn't in your personal demesne you'll take a hit.
The following is what I was talking about with the V-L Relation
Hope this helps and good luck! Sorry about any confusion!