p values in lmer using lmer Test. Running the model multiple times to get robust p values?

Question

I use lmerTest to obtain p values for my lmer models in R. Unfortunately, running the model multiple times give me different p values each time. Is there a way running the model multiple times to calculate one robust p value? Any other way to obtain more robust p values are also highly welcome.

My code (this is a model with best random structure according Aicc, interactions with high varioation inflation factor were removed):

model <- lmer(cmic~h2of+pH+TempGlob+exp.age+tree.density+log.div+
              h2of:pH+
              h2of:TempGlob+
              h2of:log.div+
              pH:log.div+
              TempGlob:log.div+
              exp.age:log.div+
              (1|experiment/site/block),data=micc2,REML=TRUE) 

Thanks S