The OM-4 and OM-2S both have higher-drain circuits which do tend to deplete batteries even while unused. HOWEVER, it is absolutely critical that you select the correct batteries for these cameras. For example, if you put Lithium batteries in it, thinking that they should be better for cold weather (usually they are), forget it. You'll get maybe two days out of the batteries before the voltage-drop lowers them below the point where the cameras will turn on. Those are absolutely no-no.
I had an OM-4 for several years, but now have an OM-4T (USA version of the OM-4Ti), an OM-2S and an OM-3Ti. The OM-3Ti doesn't need a battery to operate the shutter, but the meter does require it. I seem to be replacing the batteries in the OM-4T and OM-3Ti about the same time because I am a heavy user of the multi-spot metering capability.
The beep on the OM-4 can be turned off, that helps extend battery life. The 4t has the updated circuitry, as do some of the later 4's. Both models automatically turn on with a slight depression of the shutter release button, and turn off after two minutes of non-activity(dont touch that button).
OM-4Ti meter turns off automatically in 90 seconds but there is still baseline battery drain , VERY low in T/Ti compared to plain 4 (about 1/6th as much). Same goes when comparing OM-3 to 3Ti. Setting shutter speed dial to B/60 prevents meter from turning on if release button is depressed slightly but does not turn off the baseline battery drain. If batteries are going dead quickly in a plain OM-2, there is something wrong. Leaving it set to auto or manual has a very slightly drain but still, if using silver oxide batteries, you could leave meter on for a long time without killing batteries. John
I have the early OM-4 and it always had battery drain problems. I sent it to Olympus America twice and they sent it back with my batteries on a card with a lame excuse that I should not keep my flash in the hotshoe powered on.
Over the years, I learned the best thing for me is to use Alkaline A76's because the cost of Silver Oxide - considering my specific camera's consumption pattern - was unacceptable to me. Yes, they only last a short time. For a week in the mountains I would bring 12 cells in two separate containers. One set of 6 would stay in the middle of my pack, insulated from temperature extremes. The other set of 6 in my pants pocket. I would always need new batteries at the start. Sometimes they would die twice in a day. Sometimes cold weather would cause them to die. But typically I would hit a stretch of 3-4 days without them dying. Then they'd die on my last morning. I usually had a couple left by the end of the trip.