99 MERC SABLE - intermittent start problem

My dealer still has the car and is trying to duplicate and diagnose this intermittent problem. Perhaps someone else has wisdom that can help.
AUTO: 1999 Mercury Sable LS sedan, 24V, 58,000 miles.
ISSUE: Cranks and often ignites but idles at low (<500) RPM until engine dies.
OBSERVED SITUATIONS: - Drive car ~20 minutes or more on hwy and city. - Stop car for 5-10 minutes. Quick in/out of a store. - Return to car and try to start. - Car cranks fine, and engine may chug at low RPM, ~350. (The *sound* is similar to a flooded engine struggling to run.) - Repeat start routine, same condition. - Let car sit for 30-45 minutes and it starts and runs fine. - Three events like this in the last 45 days.
SUPPORTING INFO: - Main key ring has SpeedPass RFID stick, but condition occurs with and without this set of keys. - Heat vs Fuel Pumps is known issue. I try to keep >1/4 tank of gas in summer. - When the car starts, it runs perfectly - smooth and powerful. - Dealer replaced Fuel Pump Relay after event #2; then event 3 occurred. - After events 2 and 3, no apparent error codes when connected to computer. - There was once a PATS system error discovered in the log. - I did not think to observe the THEFT indicator during these events. - After complaining of musty smell in climate control, dealer installed "feature" that runs the climate control fan to help clear out the air chambers. - There have been four total events like this within 3 years. First event at 38,000 miles. No start, no fuel pump sound. Sit for 1 hour waiting for tow. Started right up - could have driven it onto the flatbed. Replaced fuel pump (not sure why).
QUESTIONS: - Has anyone observed (and solved) this issue? - Do fuel pumps behave intermittently or do they fail "hard" and not recover? - Any clue why time is my friend with this error? That is, what would change by letting the car sit for 30-45 minutes?
Thanks in advance! NZ
Posted to: alt.autos.ford and rec.autos.tech
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
Add image file

Motorsforum.com is a website by car enthusiasts for car enthusiasts. It is not affiliated with any of the car or spare part manufacturers or car dealers discussed here. All logos and trade names are the property of their respective owners.