Your fuel system has the ability to monitor the engine's air/ fuel ratio and compensate as you drive when it sees something that doesn't look right. When the adaptive values exceed a point (about 50%), a code will be set. You P0171 code indicates the fuel system has added a considerable amount of fuel delivery at the injectors and it may not be enough.
There are a few causes for this... Low fuel pressure, incorrect fuel (E85 for instance) and a problem with mixture sensing (02 sensor signal).
Fuel pressure is a constant 50 psi on the 2003 Caravan, regardless of engine or market. You wouldn't likely set a P0171 code unless you had lost close to half your fuel pressure, which would likely continue to drop until a stall occurred. Testing the fuel system for proper pressure is the only way to tell for sure, but if the van continues to run and accept throttle, chances are good that it wasn't a fuel pressure issue.
E85 has become a fairly common source of the P0171 code recently as it's become more available and remains cheaper per gallon. Ethanol carries some of its own oxidizer with it, something that makes it burn a bit cleaner than gasoline. The decreased energy density of the fuel requires more of it to be used as compared to straight gas, so your fuel system will keep adding injector pulsewidth until it sees something it likes... 14.7:1 stoichiometric efficiency. This can take up to 50% extra delivery.
While a great many Caravans were produced with flex fuel capabilities over the years, not all 3.3-powered units had this feature. Lacking an E85 sticker inside the fuel door indicates the vehicle wasn't a flex unit. The 8th digit of the VIN also tells you whether it's gas or flex... I'm a little fuzzy on the actual designation in 2003. A letter G at one time was used to identify the E85-compatible units, but it may have changed to a 3 in this model year. Regardless, letter R is not flex.
If you've accidentally put E85 into a non-flex fuel system, don't worry... run the van until you've dropped tank levels a bit and dilute it with gasoline. The light will remain on for a while as the fuel system recompensates, but I recommend avoiding a battery disconnect at this point. Your driveability will be much better if the fuel system is left to do its compensation while starting from the point it's at right now. Lift-throttle stalling, sags and hesitation are more likely by starting over from scratch immediately after a system reset. The MIL will turn itself off eventually (a few days) when its fuel system monitors have run and it's seen a marked decrease in additive adaptives.
Last would be an erroneous fuel system lean indication, caused by a failed upstream oxygen sensor or the signal circuit. Not a common problem with these units, it would produce a signal that mirrors a lean-running engine and trick the fuel system into adding fuel until it practically gags. Heavy soot deposits, possible black smoke, blackened spark plug tips and horrid driveability will typically come with this code when it's set in error.
Mileage will be similar with either the E85 or a bad 02 sensor signal... lots of extra fuel will be needed, but the difference may be seen at the tailpipe in the form of soot or no soot.
Write back if you have any questions.
Ooof! That's almost a tank of gas!
OK, so we can eliminate E85 (right?). If this has been going on for more than one tank of fuel and you didn't use E85, that shouldn't be an issue. PLEASE set me straight if this isn't the case.
A fresh upstream oxygen sensor somewhat reduces the chances of an erroneous signal causing this problem in error.
That leaves.. fuel pressure. Having a short honeymoon from problems like this is a symptom of a weak fuel pump at times. It can operate fairly well until accumulated heat in the tank from road surfaces and the pump itself causes it to either begin stalling or having a problem picking fuel up from the tank. The fuel pump inlet filter screen may be mostly restricted, something that can produce almost vapor lock-like symptoms. If you've noticed a high-pitched whine from the left center of the underside of the van, something that gets more shrill when it's acting up, it may very well be this filter screen that's causing your problem.
It's available separately, but the same amount of labor is needed to replace this screen as is needed to replace the whole pump module... I'd have to recommend the module.
In theory, replacing a restricted filter screen should fix this type of problem, but periods of running with insufficient fuel passing through the pump can damage it mechanically or electrically. A fresh screen might buy you some extra time, but it almost certainly will come back to visit once again. Go with a new module. You've already put the external filter on... this is all that's left.
One last thing: Let me know if this is an altered van, one used for wheelchair access or something similar. They have actual vapor lock issues due to the fuel system relocation and need to be dealt with in a different manner.