I agree with Spook.

The kickdown cable return is a spring on a little finger sized pawl in the kickdown chamber (a bit larger than a small matchbox), down inside the transmission on the left (driver) side. If a broken cable drops down, usually no problem, the pawl just hits the bottom and the broken cable end stays in place.

Shifting usually becomes noticeably retarded during accelaration when the cable breaks and the pawl stays on the bottom. If it's stuck and holds the pawl part way up, shifting will be much more normal. This may not be noticed so much in city traffic, especially with a light foot on the pedal.

The brown rubber cup on the end of the cable is just a dirt and moisture protector, and perhaps part of the reason your cable is now having problems. If the cable won't return smoothly when pulled then the cable is almost certainly frayed, often 2/3rds the way down, and will ultimately break. In the meantime, the cable will retract slowly and can unhook off the throttle spindle when the throttle is released, which sounds like what happened. Same thing if it was broken, but you'd be able to pull the end out with a bit of effort. Fraying is often aggravated by the cable eventually wearing through the lining in the cable sheath, normally at a bend, and even allowing rust to happen there, wearing on the now exposed metal coil.

Trying to lube the inside of the cable with oil often gives it a bit more life, especially when this just starts happening, but may require multiple applications into the end of the cable held vertically, trying to get it down to the fray. Being able to move the cable a little bit helps to work it down. Maybe worth trying over two days, letting the end stand upright overnight. I even once made a little cup at the top with masking tape and filled it with a bit of oil, standing it vertical overnight so it would wick down. I can't remember how many months more life I got out of it, or if I gave up with the fray being too far gone to retract easily.

Replacing the cable is a bit of a pain and a mess, but can be a DIY project. It will require removing the trans pan, which in our 700/900s means removing the rear cross member and having to unbolt the trans mount.

The dipstick tube is often frozen solid on the pan fitting and nearly impossible to get off, even with a flare wrench. I recently tried a large crows foot flare head (not cheap or easy to find decent quality metric ones) on the end of a long 1/2" breaker bar and gave up, worried I was going to damage the flange on the pan even though I had a good counterhold on it. Up on a hoist I might have been able to do it, but not lying on the ground. Many resort to unbolting the dipstick tube from the starter motor (a pain to access and needing wobble extensions and/or universal joints to get a socket on it) then drop it all down with the pan. My preferred and highly recommended method is to cut the tube in the horizontal section (closer but not too close to the bend where it's easier to get a cutter on it). A decent mini-tubing cutter will do the steel tube with enough patience (takes about ten times longer than copper plumbing). You then use a double ended brass compression fitting to re-connect the tube. There's an SAE size (5/8" as I recall) that's a near perfect fit. You can get them at places like Home Depot for fairly cheap. You will need to cut out a small section of the tube for the fitting (about a 1/2" gap as I recall). Reconnect it while installing the pan. The next person to drop the pan will be very impressed with your efforts as it will be a piece of cake next time.

You need to raise the car up a fair bit for easier access to the kickdown chamber and see what you're doing. Once you've got that far, the worst is over. Installing a new cable is fairly straightforward.

Clamp the little ferrel on the new cable after installing both ends of the cable with it in the fully retracted position, leaving about a 1/4" gap to the end of the adjuster sleeve (1/8" to 3/16" gap to the rubber cap) for later adjustment if needed.

End with a final cable adjustment (as described in the FAQ, use the pluck/thunk method in a quiet area, hoping you remembered to wipe any gunk out the bottom of the kickdown chamber so you can hear it).

Use the recommended ATF fluid, preferably synthetic. Be careful choosing a newer ATF fluid that's compatible with the Volvo spec (not all are). Let it drain overnight after you've got the pan off to let it all drip down, otherwise an initial short flush at the trans cooler line on the rad is recommended (see the FAQ).

--
Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now