You didn't mention if this is an automatic or a manual, although the other replies seem to assume it is automatic. My '83 240DL has had on-and-off overdrive problems since we have had it, about 10 years. The most common problems for us have been are:

1 - Loose wire (or entirely fallen of) on solonoid. The wire is just a spade-terminal on the side/bottom of the tranny, and can easily get pulled off by a stick, or rock, or just vibration.

2 - OD Relay, hidden behind and to the left of the glove compartment. Some of the circuit board gets kind of deteriorated, but can be fixed with a soldering iron, or a few dollars for a junkyard replacement.

3 - OD button on the stick shift. This only broke for us once. Got a new one on ebay for $1.

4 - Loose wiring inside stick shift. Just had to pull it back up and give it a little slack, so it wouldn't pull on the button connectors.

5 - Cold temperatures. When it is cold (freezing or below), the OD does not work until the tranny heats up. Usually takes 15 min of driving or so. This one is unsolved, but is likely related to...

6 - 4th gear sensor inside tranny. There is a little switch inside the tranny that closes when the stick is in 4th gear. I often have to (especially in the cold, but sometimes just randomly) push the stick shift as far to the bottom right as I can. I used to put a bungee-cord on the stick to hold it there. I think the switch is just all gummed up or something, and doesn't want to close all the way. I think the hot tranny makes the gumminess go away.

We once had to drive from NC to NY with no OD. We didn't go over about 60, which in VA means getting run off the road, but otherwise is not so bad.

-Kevin

Hi. I forgot to answer you other question, about maximum speed in 3rd if you don't get your OD fixed.

The sailboat that I usually tow with my '84 Volvo (my wife and daughter have '93's), sometimes several times a week, during the summer weighs about 1,000 lbs, and I lock out the OD about half the time while on the highway (i.e, on the upside of the hills).

Also, I occasionally have towed a ~3,000+ lb powerboat with my Volvo on the Garden State Parkway (relatively flat), mostly in OD locked out, and at 55+ mph (or else you're just driven off the road by the other GSP drivers going 70mph).
Finally, the heaviest thing that I've towed weighed about 3,500+ lbs (a big, tandem axle U-Hall densely packed) up and down the hills of CT and MA, between NJ and Cambridge, MA (i.e., Rt. 287, to 684, ... finally to Rt 90 Mass Turnpike). Anyway, to make the grades on this roads, especially with a heavy load and hilly roads, I've never hesitated to keep it locked out of OD most of the time -- that U-Haul trip to Cambridge (to take my daughter to college) was almost 100% in 3rd gear!

All of this, on highways, was maintained at 55-60 mph to safely keep up with traffic (except when the car couldn't make it up some really steep hills). I have no doubt whatsoever that 55-60 in 3rd is fine -- although I admit I haven't done this for 1,400 miles.

One thing to consider -- whereas I usually get over 20 mpg, when towing that U-Haul almost continually in 3rd, I got only about 8 mpg (a lot of stops at gas stations)! So 1,400 miles will be a LOT of fuel, although you won't be pulling a heavy trailer too, so it probably won't be as bad as that.

Good luck. But remember to be suspicious of that work that they claim your 1989 car needs! I'm not buying it.

You really didn't describe any symptoms of the problem except to say that it "lost its overdrive", so that limits what we can suggest to you -- but that vague statement could represent either a big concern, or else a relatively small matter that's being blown all out of proportion (i.e., ripping you off) by some unscrupulous parties. So let me offer the following:

Volvo automatic transmission usually have a long, long lifespan -- I've never had a problem requiring a tear-down and usually go 275-300,000 miles on the original tranny*. And for an '89 to have this problem is extremely unusual and suspicious unless it's been badly abused or overworked (e.g., pulling a heavy trailer through the Rocky Mts. without a good fluid change before and afterward, etc.)
[ * and I should add that I'm not easy on transmissions -- I typically drive hard, accelerate fast, shift manually a lot, keep the revs up, etc. Also, I use my Volvos to repeatedly tow a boat between my backyard and the lake during the summer.
On the other hand, I also use a good brand of synthetic ATF.]

I have, at times in the history of my cars, had overdrive problems occasionally, however. In every case, the transmission wouldn't shift up into 4th (the OD gear) -- it would shift normally but only as high as 3rd -- and the dash light would stay on all the time.

I sincerely hope that the above isn't your symptoms (i.e., shifting normally up to 3rd, and with the dash light on), because if it is, you're being taken for a "ride"!
Especially so if the light is staying on as part of your problem ... they're telling you that the problem is inside the transmission, but there's no way that the light's circuit would know that and stay on because of that -- it only reflects problems in the electrical control circuit, including shifter pushbutton, relay (under the dash), solenoid (mounted to the transmission on the outside) and the wires between these parts.

The problems of the above (the symptoms I described) are usually, in order of frequency:
1) bad overdrive relay (under the dash) -- most common ΐnd easiest thing to fix]
2) bad wiring (insulation bad) between shift pushbutton and solenoid -- uncommon and cheap to fix, but awkward to reach to do the work, and not likely in such a young car.
3) bad solenoid -- much less common than these first two, but expensive (the part) and difficult to do (but it's still not a transmission tear down!).
4) bad pushbutton switch on the shifter -- cheapest repair, and easiest, but also least likely to occur.

So, if your symptoms are as I described them here, take your car elsewhere!

If, on the other hand, your symptoms are different than I've described above, that's another matter -- with which I admit not being familiar.