An aftermarket BOV which vents out into the open will often cause this problem... that's why I mention it.
Check for diagnostic error codes and report back. As there may be old codes stored in the system, you should check and write down any that are already there. The, pull the EFI fuse for about 10 seconds and put it back. Drive the car a couple times and once the problem has occurred a couple times check for codes again. Post back with both the codes from before the reset and also the second set of codes (if any).
Check the intake piping and rubber couplers VERY thoroughly for any cracks or holes; This sounds allot like an intake leak. How well does the car idle?
How to pull codes from the eCU:
http://www.cygnusx1.net/Supra/TechTi...ror_codes.aspx