Also, proton decay is a thing. At a certain point, if the proton is unstable, the half life of the nucleus is longer than the proton itself.
There are extensions to the Standard Model being used to search for dark matter, but until one of those is actually found experimentally, you can't say that it makes the Standard Model incomplete. It's sound within its domain -- aggravatingly so, since that makes it really hard to figure out what's next.
But similar to your example, neutron decay is a thing (a free neutron has a halflife of about 10 minutes), and yet many nuclei are stable for much longer.