Water absorbs electromagnetic signals (at some point, including light). That's why the only really effective way to look for something under water is sonar (loud sound/pressure waves), and even that has a limited range. That, together with the ocean being so big, is why military submarines can hide so effectively.

A radio transmitter or radio beacon on board of the submarine wouldn't work because the water would block the signal. However, the submarine could use a sonar beacon, like the ones used on airplane black boxes. The standard ones have a range of several kilometers, but there are low-frequency ones that transmit pulses at 8.8 kHz with a range of 10-30 km (search for "8.8 kHz beacon"). The answer why they don't use that seems to be simple: They don't have it. - why they didn't install it is a good question. The beacons are able to handle the depth too.

One problem with underwater sonar can be layers of water that have different densities (e.g. due to being saltier and/or warmer/colder). Sonar/beacon pulses can be reflected by those, which could possibly make such a beacon less effective.