An 88 honda civic wont stay running

I've answered this Sergio. Maintenance is key. When was it last serviced?

You need to run a system fault code test, do that by following the instructions HERE, code are also listed at the site.

Not that I know of.
Are you getting spark to the plugs when it won't start, and how long do you have to wait for it to start ?

You need to check for spark,disconnect one sparkplug wire and ground it about 1/4 inch from the engine graound and have some one crank the engine. If there is spark then you have a fuel issue,and you will need to check the operation of the fuel pump if there is no spark then you will need to inspect the ignition switch, your make and model has a high ignition switch failure.This will include ignition coil and cap and rotor.Your Honda also has a high failure rate of the ignitor which is in the distributor

It sound like you have a bad relay. Its getting hot and has to cool before your car starts. Its probably the EFI main relay.For a guide on checking the relay CLICK HERE

check your distributor cap and starter fuse

most likely u burnt the coil
check for spark at the spark plug leads
no spark burnt distributer
change it

what about the distributor pickup? have u replaced that, also pull the steering column covers and see if the ignition starter swtich has come apart, very common on this year.

it sound like you have a bad distributor, good luck.

try changing the main relay under the dash