“being tired” is a legitimate reason to not want to hang out, it is also an easy excuse with no descernable evidence. Used once it’s believable, used lots of times it starts to “feel” like a fake excuse or even a lie.
If your friend thinks you complain about being tired a lot, they are (very likely) trying to say that you’re not putting the effort into the friendship they believe they deserve out if you.
As has been said in other comments, it might help to give examples of times where you’ll be less tired. Or just invite that friend out at those times.
A friendship dies take effort from both people to maintain. Breaking your cosy sofa time is effort, but if the friend means enough to you then you will sometimes make that effort to see them.
Brother