Yes, this sounds like an error produced by the submodel fitter during the projection. Unfortunately, to fix this, a reproducible example is needed (and some session info, at least the projpred version).
For GLMMs, there have been some updates to the submodel fitting in the develop branch of projpred. You can install it via devtools::install_github("stan-dev/projpred", ref = "develop"). Perhaps this solves your problem?
All this (although the middle point probably doesn’t matter) gives the broad hint that the problem occurs when fitting the multilevel submodels. So it’s related to the lme4 package. The only way I see to fix this is to have a reprex and then to play around with lme4 tuning/control parameters. The develop version of projpred allows to pass arguments to lme4::lmer()/lme4::glmer() (former one for a Gaussian model, latter one for binomial and Poisson models). If you can’t provide a reprex, you would have to play around with lme4 tuning/control parameters yourself. I’m sorry I can’t give a better solution.