Here is my rudimentary explanation.
There are different kinds of DC motors, shunt wound, series wound, permanent magnet, and more. I know you can regen with permanent magnet. I'm pretty sure you can't with series/shunt wound.
With a series motor, you have a coil on the case and a coil on the armature (shaft that spins). You put power through the case coils and the armature coils to produce power. You put in more power, you get more power out. Shunt wound motors are similar in that you have a coil on the armature and case I believe, but are wired differently. There are other incarnations of DC motors too, but I don't know enough to explain them all.
With a permanent magnet motor you have magnets on the armature and coils on the case (brushless), or magnets on the case and coils on the armature (brushed permanent magnet). So you put power into the coils and they push against the magnets. This limits the power of the motor since the magnets can only push back so hard, but makes it more efficient. But, it allows you to pickup the magnetic field when the magnets pass over coils.
Without a magnetic field to pass over a coil, you can't make electricity. So with a series wound you'd have to put power into one of the coils to get power out of the other coil. The net effect would be a loss in power since its not 100% efficient.