Assuming you're not talking about the normal exposure interval delay in closing the shutter after opening it, you should never experience any noticable delay in opening the shutter after pressing the shutter button unless:

• Your batteries are low.
• The self timer is slightly engaged.
• There is an electrical fault in the metering system.

The batteries should last 1-3 years for a pair, but I've seen odd behaviour like this with my FA when batteries are very low, so check that first, then play with the self timer.

Now, a few points on FA shutter release behaviour:

• When in M or A exposure modes, the camera uses a mechanical shutter retard mechanism. This requires an additional 1-2mm of movement on the shutter release button before it releases the shutter. This is normal and doesn't delay the shutter release as such; it just feels and sounds slightly different.
• When in P or S exposure mode, the FA uses an electronic shutter retard mechanism, which is slightly quieter than the mechanical one and the shutter button requires less pressure to release the shutter.

I hope this helps, as the FA is a terrific camera and excels at low light auto exposures.