Are HPS lamps with air inside still usable? I have one that might have a vacuum leakage.

Won't warm up as much with air and the seals will oxidize after a while because of oxygen in the air reacting with them.

I think this is the failure mechanism of the chinese Osram NAV(SON)-E we have in Qiryat Ata, as when they cycle (Temporarily), they restrike at much lower pressure than most HPS lamps (There is one at the first lantern of my street, that shows a glow discharge in the outerbulb during its two cycles, as a result of a slow air leakage), finally turning ON and OFF at orange color for a long time before finally reaching full brightness. and than dimming to orange color and stop working at the same night they began to dim to orange color.

Has the gas getter gone white ( normally it's the shinny silver spot on the glass ) if it has, you have air in the tube, but you can burn them until they die if you like, they will fail and sodium's generally fail gracefully, unlike metal halides, and you might not get it to full brightness but I've seen lights running missing the entire outer envelope, how long they last I can't say you would need to ask the kid with pocket full of marbles and the sling shot to ask them when they smashed it, maybe a year, maybe a day...