I don't mean that it would degrade the battery, just that playing Hi-Res files uses more power than regular CD-quality files do. So, say you were only playing CD-quality files up until two week ago and you were getting 4 days of playback on a charge, then you switched to Hi-Res files. You would expect to only get 3, or maybe even only 2 days worth of playback time on a full charge (depending on how much of that battery life was split between playback and standby). As a matter of fact, if you switched to higher-quality files, or even just that you now have new music to listen to, you might also be listening more often or for longer periods of time.
In any case, if your battery life dropped near the same time you changed the quality of the music files, it would make sense that the battery life issue may be caused by the quality change. Also, as noted by
@kismetsky, if you turned on Bluetooth at some point or used NFC to pair your A45 with a Bluetooth device, you might want to go back and turn NFC and Bluetooth back off when you aren't using wireless devices with the DAP. Even if the device isn't paired, it will be using battery life to keep the Bluetooth controller and radio turned on (if it has been paired with a device, it uses even more battery while it periodically searches for paired devices), and NFC is always sending out radio beacon-like pulses to try to discover other NFC or RFID-enabled devices nearby, so it is slowly using extra battery life, too.
None of these situations would mean that the battery has suffered any loss of functionality, it's just that the amount of battery you are using has risen, so your battery just gets drained faster. Even using the device outside the "sweet spot" of 40-80% battery life isn't going to suddenly degrade the battery. Lithium-ion batteries have 500~1000 charge cycles, and the 0% battery that the DAP reports is not 0% remaining charge on the battery. It is just that the battery is considered "empty" at 3.2 volts or so. The player isn't going to allow you to drain the battery to a dangerously low voltage, and there is going to be a decent amount of "padding" built into the battery monitoring circuits so that 0% on the DAP's screen is still well within safe limits. The only way to discharge a battery in the DAP to a dangerous level would be if you drained the battery until the DAP shut itself off, then stuck it in a drawer for a month or two without charging it. While the battery sits not being charged, it will very slowly lose charge, and it will eventually get down to the point where it can no longer be recharged, or if you charge it just in time, it will have degraded so that it now has a lower maximum capacity than when you bought it. Unless you let it sit for a long time at 0% and didn't charge it during that time, I highly doubt that the capacity of the battery has been "suddenly" damaged.
The only other situation where a battery could be damaged would be if there was some sort of manufacturer defect in the battery protection or charging circuits. If the DAP allowed the battery to be charged "beyond 100%" or discharged "below 0%" then damage could occur, and that could cause battery life to be impacted.