Hi Dave
If any battery weather it be a car, backpack, or any other type of battery is used in what is known as a cycle mode,ie constantly charged and then used until flat, then the battery will last only 2 thirds of its expected life. as you said 13.8v is a fully charged battery,and this voltage is also correct for a car battery.
dave if you charge your battery until fully charged, and then you use your multi meter to check the voltage, this can lead to a false reading.
fully charge your battery and leave to stand for at least half an hour to settle to its correct voltage. and then take a reading, if it has dropped below 13.8 then your battery is not holding its charge.
I used a 12v battery tester, and a testers can be bought from your local motor stockist, what these testers do is put the battery under load and test it that way.
Another good way to put your battery under load is to connect a car cigarette lighter to it, this will put your battery under load, give it a few minutes to settle and then take a reading with your meter, after a few minutes your battery should have recovered enough to give a steady reading of about 13.5v-13.8v if any lower again your battery is not holding its charge.
I used to be an alarm enginner, and the 12v battery's were tested the same way as above, now a battery in cycle mode could last a year to 18 months, but a battery in stand by mode could last up to 4/5 years, you can see the difference between cycle and stand by modes.
If you bought yourself a multi meter, you can connect your meter between your pump and battery, and do a current test on it, read your instruction manual on the way to do it, this will give you a reading of what your pump is drawing from your battery, and give you a good indication on the condition of your battery.
I could write pages on battery's but will only boar you. if you need a paticular question answered give me a shout, and i will be happy to help.