Oil pressure light at low RPM

Before you have major repair done on your car because of the "oil pressure light", review the list and see if any of these might be the source.  Some of the things on this list are things you can do yourself, some only done by a mechanic (inexpensively), and others require the aid of a mechanic.
1.  Check to see if you have a leak.  Low oil levels can make the oil sensor light come one.  Check your oil level following the manufacturers recommended procedure or use the information listed here http://autorepair.about.com/od/regularmaintenance/a/checkoil.htm.  If you do not have a low oil level, but still suspect a leak, place a drip pan under the oil plug overnight.  If you have a leak, you'll see signs of it there.  Then take the vehicle to a trustworthy mechanic and let them trace the leak.  It is possible for your engine to only leak when it is hot, so make sure you get the engine nice and warm before you put the car away for the evening and place the drip pan under your vehicle.  Other signs of an oil leak are listed below as well as an "oily" exhaust that leaves it mark on your bumper or "blue smoke" as you drive/idle.
2.  Check the coolant levels. If the coolant is low, the oil will heat up faster and cause a viscosity breakdown.  When the oil viscosity is low (= thin oil), the oil sensor light can come on.  If the coolant is low, add more.  Keep in mind that an engine running hot will heat the engine oil to the point that it thins out and burns off in the cylinders.  If the coolant level is fine, have the coolant (water) pump checked.  If the coolant is not circulating well through the engine, you'll probably have coolant boiling over, too.
3.  If you can afford to do it, change your oil to a higher or lower viscosity.  Refer to your maintenance manual and your trusted mechanic. I say this because, if your oil is thinning out too much because the viscosity is too low, your "check oil" light will come on.  If your engine oil is too thick, you engine will need added internal pressure to get it to circulate.  At lower RPM (just like thin oil), your engine oil light will come one.
4.  Have the oil pressure checked by other than an electronic means.  Your trusted mechanic can place an oil gage between your oil filter and the rest of the engine or on the oil fill cap of the engine.  If you are having an oil pressure problem that is seal-related, that should narrow it down.  If you can't afford to do that, when you get your next oil change, replace: the oil fill cap, PCV valve, and air filter.  All these contribute to the measurement of engine oil pressure by that picky little oil pressure sensor.
5.  Have the oil pressure sensor checked.  You may need some weird add-on to make it behave.  Do a search for the following part and read and you should have a better understanding: "part # 05017800AA a terminal/wire/vent to the oil pressure switch connector".  Never forget that sensor are usually engineered to report a problem well before a catastrophic failure can occur.
6.  If you're driving a high-milege car, make sure you are up to date on all of the engine-specific services.  For some vehicles, it is recommended that the head gaskets are replaced.  If you have internal engine leaks because of it, this will solve most of those issues.  Signs of this include: coolant visible in the crankshaft area (you can see this with the oil cap off), oil fouling your coolant (you can see this in the coolant reservoir), or smokey exhaust.  Expect your trusted mechanic to recommend that you change your spark plugs, timing belt, and cam shaft gasket at the same time.
7.  See if the oil pump needs to be replaced.  A faulty oil pump can contribute to low oil pressure as it fails (but hasn't failed, yet).  
8.  Do all of the above BEFORE you take to recommendation to have your engine replaced.
I have a 1998 Chrysler Cirrus (I know it's not a minivan, but hear me out).  I've been the single owner and have learned more about how engineering oversights or over-cautiousness can send you to the mechanic for just about everything.
Hope this helps!

The 1999+Dodge Caravans have several problems in the 3.3L engine, but also may be present in the 3.8L as well. One of them are bad oil pressure sensors. They leak and or give false readings. First thing to do is check your oil level and condition of oil, dirty, milky, etc. If you are still getting an oil light and chime at warm idle, change the sensor. Cost me $20.00. I also went to a 20w-50 for insurance on
a higher mileage engine in a temperate climate. No problems ever since. Seeing the light and hearing the chime are a heart stopper.

        Packer77 here. As I suspected it was my oil pressure sensor . It's been over 2 weeks since I replaced it and all is good. I would check to see if the sensor is showing some oil leaking, this was my situation anyway.

       Hope this helps.

Did you shut it off and check the oil, it could be low