DIAGNOSIS The reciprocating saw is a power hog, but a drastic drain points to the tool working too hard. The most common cause is a dull blade. A dull blade requires exponentially more motor effort (and battery amps) to push through material.
FIX Check your blade first. Is it the original one you've been using for months? Swap it out for a sharp, new blade designed for the material you're cutting. For demo (nails, wood), use a coarse tooth demolition blade. For metal, use a fine-tooth bi-metal blade. You'll be shocked at the difference in battery life and cutting speed.
IF THAT DIDN'T WORK If a new blade doesn't help, the tool itself might have a problem causing excessive drag. A failing bearing in the gearbox or a misaligned counterweight can create internal friction that the motor has to fight, pulling huge current. This requires the internal inspection mentioned in the grinding noise fix.
HEADS UP Also, make sure you're using a high-capacity battery (5.0Ah or higher) for this tool. Using a small 2.0Ah or 3.0Ah battery will get drained very quickly under the saw's normal load, and that's expected, not a fault.