How long can food last if reheated periodically?
Yes, it will "make it last longer in the fridge" for a certain definition of "last longer": it will not mould nor infect other foodstuffs in the fridge if it doesn't come into direct contact with any of them.

Is it still safe to eat after a few of these re-heatings? Very probably not! 

Elaboration: More then half of the number of cells in your body are actually bacteria; bacteria don't generally kill you but the toxins they release is what kills you.  E.g. Botulinum Toxinum D (one of the toxins released during Botulism) has an LD50 of 0.4 ng/kg, which means that you need about 500g (a pound) to kill 99.9% of all human beings on the entire planet...

(And that is for just a few re-heatings; for "nearly indefinitely" we need to bring extremophiles in the equation...) 

Related, but not identical question