Imagine you're in a funk-rock band whose drummer often fails to show up for rehearsals and gigs. That would be an intolerable situation, because all the bands' efforts come to nothing if the drummer isn't there to perform.
Though it might be painful for the band to admit it, you'd actually be better off rehearsing and performing without the drummer. Sadly, that probably means doing a different, less propulsive style of music. In the music world, professional doesn't mean "louder and flashier," it means that you showed up on time and did what you said you were going to do.
In much the same way, if your creative work depends on inspiration showing up, you're in trouble. Inspiration is not a reliable partner. Sure, you've done some amazing things when inspiration showed up, but you should also have some way to work even when inspiration is nowhere to be found.
It's easier to do this if you don't try to compete with your own best work. Just aim to create something simple that convincingly fills its space. As a songwriter, you can always put stock chord progressions together with standard beats and craft some competent rhyming couplets. You can tinker with the results and patch up any weak spots. And if the song still fails, you can throw it out and start over as many times as you need to.
You don't need inspiration to practice your songwriting craft. Sure, your results will be more modest and the work will move more slowly without the help of inspiration. It doesn't mean you've failed as an artist. It means that you're a professional, and you're showing up and doing the gig no matter what.