Sudden Oil Loss

My Dad has a 2002 Accord LX 4 cylinder (45,000 miles) and has been in two accidents over the past 3 years where there was front end damage.    
 
Here is the problem: He is experiencing sudden oil loss with no visible leaking on the ground.  Usually if you have an oil leak or are burning oil the oil is all over the exhaust or back of the car.   He can drive 1000 miles with no loss of engine oil and then have a significant drop in crankcase oil in a 200 miles.  Not sure where the oil is going.
 
Any help would be appreciated!   Thanks!
 
 

I'm having the same problem with my 2001 Accord EX as we speak. I have yet to find where the oil is going. There are no visual leaks on the ground but I noticed just the other day smoke coming from my exhaust. It's not much but It's still smoke...

If you're losing oil with no sign of external leakage, then the only place you can be losing it it is out the exhaust pipe, i.e you're burning oil. There are three possible causes, worn oil control rings, worn valve guides / seals, blowing oil out of the crankase breather into the plenum chamber (which would be associated with excessive 'blowby' gasses from worn compression rings). You can burn enough oil to be seeing oil level dropping on the dipstick, but still with no obvious smoking.

None of these are easily fixed, but you may be able to lessen the symptom by using a thicker grade oil, and / or one of those 'stop smoke' products (which are basically a very thick oil added to the existing oil to thicken it up). Personally I'd just live with topping the oil up when needed unless the engine starts to blow obvious smoke. Using a thick oil will typically adversely affect fuel econmy and power to some degree, but, if the compression rings are sealing poorly may actually improve ring seal and cause an improvement in economy and power...
 
PS The rings may be stuck in the ring grooves rather than actually worn. This would be the result of gummy deposits between the rings and grooves preventing the rings from being pushed outward against the cylinder walls by compression and combustion pressures acting behind the rings. You could try a product designed to clean rings / grooves, such as 'Auto-RX' or 'Seafoam' etc... There is a lot of info on such products on the 'Bobistheoilguy' website.

Often times on a car that is "newer" like that you can start burning oil and not see blue smoke for quite some time.  The cat, and the exhaust do their job and "filter" the smoke so you don't see anything, then seemingly overnight the car starts emitting a big cloud of blue smoke because the cat and exhaust are now to "coated" to filter it properly.