` My 10 year old iPOD will not hold a charge for more than 45 minutes.

Apple will replace the battery or give you an identical model refurbished iPod with a new battery for $79US plus shipping. See: https://support.apple.com/ipod/repair/service

While the battery can be replaced it will not be able to be done by Apple.

You will have to find a third party technician if you wish to have it done. The cost of finding a newly manufactured battery as well as a technician who is able to replace it may be more expensive than it's worth.

That would typically be the case except you failed to notice that the user states that their iPod is 10 years old.

I did see that. The OP probably has an iPod 4, which, as far as I can tell from the link I provided is "an eligible model" for a battery replacement.