Mixed model Beta distribution fit diagnostics


I have a split-plot design and I want to test the effect of 2 factors on the disease incidence (continuous proportion). I am using Beta dist. which is appropriate for these data (bounded within 0-1).

The fit statistics look OK (Pearson Chi-square/DF close to 1)
Fit Statistics for Conditional Distribution
-2 log L(Rust_DI | r. effects) -602.65
Pearson Chi-Square 133.25
Pearson Chi-Square / DF 0.79

My problem is that residual plots look bad (please see attached).

Any comments on these plots?
Any suggestions would be greatly appreciated.