Testing Chinese CR2032 Li-ion Battery Capacity
CR2032 batteries are simply not intended for high current. They are lithium/MNO2 chemistry, which makes them lithium, not lithium-ion. For the behavior of a reputable source, see here, for instance where pulling a pulsed load of 23 mA produced about 1/2 volt drop in the output voltage. With that said, your nominal 37 mA isn't that much greater, so I'd expect something on the order of 5 hours duration for your test. 

You need to test at much lower currents, like 1 mA max, and take your time. Your nominal 2200 mA-hr would last about 9 days at 1 mA, but even this is stressing the battery. From the web page, a 100 ohm load (about 3 mA) will pull down the battery voltage by half a volt in a few seconds.

EDIT - As Ecnerwal has pointed out, the battery was rated for 220 mA-hr, not 2200. My bad - brain fart.  As a result, I'd expect something on the order of an hour or 2 for 37 mA, so low-current testing is still a good idea. At 1 mA, 220 mA-hr is 9 days, of course.