If the model is not significant when two predictors are entered together, could it become significant if they are entered separately? These predictors are highly correlated.
In another (significant) model, when the predictors are ran separately, one of them accounted for higher unique variance (around 40%) than the variance accounted for when they were entered together (around 10%). I am also wondering why that is?

If including the second variable improves the fit only a tiny amount, yet the degrees of freedom change, that could happen.
I find it easier to take this to the extreme. Add in one variable that really matters and a bunch that do not, say 100. Those 100 irrelevant variables will contribute to the degrees of freedom in the $F$ or $\chi^2$ distribution, making quite high the threshold for model improvement to be significant. However, those 100 irrelevant variables make little difference to the model fit, not enough to make up for the degrees of freedom. Thus, those $100$ irrelevant variables wash out the real effect of the one relevant variable.
For just two variables, the same idea applies, just less dramatically.
