I presume it's not leaking any hydraulic fluid. If it is, this will not work. Close the valve as if you're going to lifting something with it. Without any load on it, raise the jack to full height and continue pumping the handle about two dozen times. Then see if it will hold a load without sinking. This is a very old trick that works more often than not with jacks that aren't leaking hydraulic fluid. Did a Lazarus act on a two decade old Test Rite (sold by Sears) with this in early January. Hasn't been a temporary fix either. Been using it for two months now lifting half its rated load without so much as a millimeter of sinking. Left it with half its rated load for a week to test it.
All that said, I will NEVER work under a load held up only by a floor jack. I use jack stands with that Old Time Religion. All that's needed is to know about one instance of jack failure and you will also get that same Old Time Religion. Only time I've ever worked without jack stands is changing a flat tire by the side of the road, and once in the military putting a new front wheel bearing on a M151A2 out in the middle of nowhere using its jack, and that didn't require getting under it.
John