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It's not so much a case of the transponder being turned off, it's a case of not being in range of a receiving station. Remember, these rigs operate a long way off shore. According to Wiki,

Shipboard AIS tranceivers have a horizontal range that is highly variable, but typically only up to about 74 kilometres (46 mi).

Sometimes you get just the right atmospheric/ionospheric conditions to get detectable transmissions well in excess of this range. The change in weather and ship position will give "windows" when the ship is visible.

A lot of AIS receive stations are run on a volunteer basis. You could set one up yourself if you want - though not much point if you're not near the coast. A ship disappearing off the coast of Senegal could mean that the only receiving station that is in range has been turned off. No idea how reliable the electricity network on coastal Senegal is.

And yes, a subscription to Marine Traffic will give you the satellite AIS fixes.

The wiki article linked above will give you a much better handle on the limitations of this system.