It looks like the only unusual things about the original Hall sensor are (a) it has a maximum output current rating of 400 mA, but I doubt that the connected circuitry would require this, and (b) it has two complementary outputs, but from the markings on the circuit board, it appears that the design may be using only one of the outputs anyway. Check this by looking at the tracks from the sensors to the socket on the board. If only the OUT1 pin is used (the one next to the positive supply pin), then it's compatible with a standard Hall switch.
It doesn't contain a "frequency generator"; I think those words in the data sheet refer to the fact that it will generate a frequency if exposed to a rotating magnet. Well, duh!
The original claims to be temperature-compensated, but given its wide magnetic tolerance and hysteresis, and the application, I don't think that's important.
The original one is unipolar, activated by a south pole only, but AFAIK you could also use an omnipolar device.
The original device has a wide power supply voltage range, but according to the PCB markings, it's being operated at 5V so that's not an important factor either.
Its physical characteristics (e.g. thickness, location of the sensor) may be significant, especially if the sensor is clipped into some precise fitting. If not, you could try a replacement sensor in a known good unit. It's very unlikely that any harm would come from it. You want one that will activate at (or slightly below) 150 gauss (15 milliteslas). Here's a Digi-Key filter specification:
http://www.digikey.com/product-search/en?FV=fff4001e,fff80480,4000db,40308a,40393b,a401cc,a401d7,2dc07df,2dc08be,2dc0ef2,2dc11b6,2dc17f2,2dc1818,2dc1819,4500011,450002f,4500188,4500351,450056a,450080f,10180001,10180043,1018004c,10180050,10180051,10180141,101802a8,101802ab,101802b1,101802e4,101802e5,1180000c,1180000d,11800019,142c02ca,142c03c0,142c09c5&ColumnSort=1000011&stock=1&quantity=1
Any of those should be suitable. If you want a specific suggestion, try the cheapest one:
http://www.digikey.com/product-detail/en/US5781EUA-AAA-000-BU/US5781EUA-AAA-000-BU-ND/1485720. Download the data sheet to work out the pin connections because they're different from the original. I think you need to mount it wide face downwards, because the back is sensitive to the south pole.
Good luck!