Check for diagnostic codes:
http://www.cygnusx1.net/Supra/TechTi...ror_codes.aspx
A couple possibilities exist:
"Fuel cut" where the ECU cuts the signal to the injectors because it thinks or you are moving far more air through the air flow meter than there should be at a given RPM and throttle. This is a protective measure to prevent damage (see: engine meltdown). The most common causes of this are: a leak in the intake piping AFTER the air flow meter; increased boost pressure, whether intentional or due to malfunction.
NOTE: This is NOT what Toyota meas when they refer to fuel cut in ANY of their tech publications and service manuals.
Engine knock... not necessarily rod knock... inconsistent or premature ignition of fuel causes knocks which the ECU monitors for and adds fuel and pulls timing to eliminate. If you've got a bad knock (from running loo low of a grade of fuel, for example) or if the knock sensor(s) and/or it's wiring is bad the vehicle can falter severely and even become barely drivable after a while (see: limp mode). BTW, hot air makes knocking all the more likely... if your cone filter is in the engine bay either relocate it so it's outside of the engine bay or put the stock airbox on and use a good filter in it (NOT Fram).
Other possibilities include: bad igniter, bad coil pack(s), incorrect spark plug gap, fouled spark plugs, damaged ignition wires, oil leaking in around the spark plugs and wires from the valve cover.