Must Remove the battery & then reinstall it to get camera to turn on.

My Canon Powershot SX40 HS camera will turn on only once per battery insertion. i.e., put battery in, the camera turns ON OK. Turn camera OFF, then press the On/Off button and the camera will not turn on a second time. Take the battery out, put the same battery back in, press the On/Off button, and the camera turns ON and everything works fine again. Turn it OFF once more and it won't come back on until the battery is removed and then reinserted (same battery). I've also found that once the remove/insert battery cycle has been performed (i.e., camera now ready to turn on), pressing the Playback button will turn the camera on, just like the On/Off button does.

Does anyone have any idea as to what is causing my camera to act this way?

Incidentally, I do not have any history with this camera -- I just recently (April 2017) bought it used. Since it did not come with a battery, I bought a supposedly compatible Vivitar VIV-CB-10L battery; the manufacturer's battery is a Canon NB-10L. Once the camera is On, it seems to work perfectly so I think the Vivitar batteries are OK for the camera.

UPDATE 04/30/17 -- Since originally posting my question, I've learned that once a fully charged, installed battery's charge becomes even slightly depleted (say the battery status icon lights only two of the three divisions of the icon), the camera will power on consistently, just like it should, without me having to remove and then reinstall the battery between power on's. So I'm slowly uncovering more symptoms but still cannot formulate a diagnosis. All thoughts will be appreciated.

Oh, and I have purchased a genuine Canon NB-10L battery (from B&H Photo) but still have the problem.

UPDATE 07/16/17 -- EUREKA! I found the culprit -- my aftermarket (cheap) battery charger was overcharging my camera batteries to 8.4 volts. Apparently the camera's electronics have an "overcharged battery" threshold of about 8.2 volts. If a battery is installed with a voltage above the threshold, then the camera will not power up again until it senses that the battery has been swapped out. (It has to turn on once in order to sense an overcharged battery; that's why I was having to remove the battery and then reinstall it to get the camera to come on just the one time per battery swap.) Of course, if the replacement battery is also overcharged beyond 8.2 volts, the "new" battery will only give you one turn on cycle of the camera, too. Since I was using the SAME battery when doing the battery "replacement", even turning the camera on just once would dissipate the battery's charge somewhat. Eventually, repeated uses of the "Install battery/turn camera on/turn camera off/uninstall battery/reinstall battery/turn camera on" process dropped the battery's voltage to below the camera threshold of 8.2 volts, and at that point the camera would begin to operate normally. Though my theory is only conjecture as to what logic is actually built into the camera, I do know that using a properly charged battery allows my $10 camera to work normally. Needless to say, I've abandoned the aftermarket charger in favor of a genuine Canon charger that I bought for charging my NB-L10 batteries.