For starters, have you verified that your battery is good? Do you have an Autozone or someplace that will check/test batteries for free? A blown cell might be providing a low-voltage starting condition. Once the car is running, the alternator will pick up the slack. Restarting later in the day would be easier since the engine is already warm and the battery was recently under charge from the alternator.

If the battery is not the problem, I would go right down this list:
1. Clean contacts on the inside of the distributor cap and rotor tip.
2. Remove and verify that the spark plugs are clean. Replace if dirty.
3. Replace the 25 amp fuse and holder in the engine bay with a new waterproof fuse holder and a new fuse. Solder in the new one and seal it with electrical tape or shrink tubing, don't just crimp it.
4. Swap your main relay with a known good one. I had a 'delayed' start problem with my car that was being caused by a main relay that was slow to engage.
5. Clean your IAC valve and test it for good operation. If this is clogged or dead, you will have starting problems and typically a slightly low idle along with a rich mixture (that will foul your spark plugs). If it fails in the open position, you will have a lean mixture at idle, starting problems, and possibly a fast idle speed.
6. Test/Replace your temp sensor (the one that sends its signal to the computer). There's two temp sensors, one for your instrument cluster gauge, and one for the computer. If the one that sends it's signal to the computer fails, you'll have starting problems and rich/lean idle situations depending on how it failed.
7. Check/replace the inductive pickup in the distributor. This device tells the ignition computer when the engine is at the proper point to fire ignition coil.
8. Lastly, check/swap the AMM for a known good one. It's a long shot, but it may play a role in your start/die situation.

God bless, and I hope it's one of the above mentioned possibilities.
Fitz Fitzgerald.
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'87 Blue 245, NA 223K