[R-sig-ME] Beginner help for mixed effects model

[Isabella Mandl]

Dear all,
I apologise for the rather simplistic questions I am about to ask but I 
am very much at the beginning of my analysis and have only just worked 
my way through to mixed effect models in R. I collected some ecological 
data over the past years and have been advised by my PhD supervisors to 
use a GLMM. It should have been rather straightforward:
I have measured "looking time" in response to different playback stimuli 
(0,1,2,3) in a group of 13 individuals - measures were repeated four 
times over the year. I now wanted to look at the effect of Stimulus 
Type, Season and Sex on "looking time" as well as look at whether 
different sexes have different looking times in different seasons 
(sex-season interaction). Random effects are ID of the animal and Trial.
This is the model I built (using lme4):

glmer(LookingTime~Stimulus+Season*Sex+(1|ID)+(1|Trial), 
family=Gamma(link="log"), data=playbacks)
which gives me the following output:

Generalized linear mixed model fit by maximum likelihood (Laplace 
Approximation) ['glmerMod']
  Family: Gamma  ( log )
Formula: VigilanceTowardsAdjus ~ Stimulus + Season * Sex + (1 | ID) 
+      (1 | Trial)
    Data: playbacks

      AIC      BIC   logLik deviance df.resid
   2731.9   2775.1  -1354.0   2707.9      258

Scaled residuals:
     Min      1Q  Median      3Q     Max
-1.4529 -0.5723 -0.0321  0.6412  2.1003

Random effects:
  Groups   Name        Variance  Std.Dev.
  Trial    (Intercept) 3.985e-01 0.6313040
  ID       (Intercept) 6.185e-08 0.0002487
  Residual             4.464e-01 0.6681655
Number of obs: 270, groups:  Trial, 135; ID, 13

Fixed effects:
                                        Estimate      Std. Error   t 
value     Pr(>|z|)
(Intercept)                       3.425875   0.184784  18.540 < 2e-16 ***
Stimulus                           0.181798   0.036725   4.950 7.41e-07 ***
Season[T.ED]                   0.382235   0.259361   1.474 0.1405
Season[T.EW]                  0.338762   0.259361   1.306 0.1915
Season[T.W]                    0.138404   0.259609   0.533 0.5939
Sex[T.M]                           0.207001   0.272354   0.760 0.4472
Season[T.ED]:Sex[T.M] -0.649771   0.387518  -1.677   0.0936 .
Season[T.EW]:Sex[T.M] -0.428328   0.378500  -1.132   0.2578
Season[T.W]:Sex[T.M]  -0.008209   0.385262  -0.021   0.9830
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
             (Intr) Stimls Ss[T.ED] Ss[T.EW] Ss[T.W] S[T.M] S[T.ED]: 
S[T.EW]:
Stimulus -0.204
Seasn[T.ED] -0.684 0.004
Seasn[T.EW] -0.684  0.004 0.486
Season[T.W] -0.681 -0.003  0.486 0.486
Sex[T.M]    -0.651  0.004  0.463    0.463 0.463
S[T.ED]:S[T  0.458 -0.002 -0.669   -0.326   -0.325 -0.703
S[T.EW]:S[T  0.468 -0.003 -0.333   -0.685   -0.333  -0.720 0.506
S[T.W]:S[T.  0.457  0.011 -0.327   -0.327   -0.664  -0.707 0.497    0.509
convergence code: 0
unable to evaluate scaled gradient
Model failed to converge: degenerate  Hessian with 1 negative eigenvalues

The model fails to converge and gives me the following residual plot 
(which to me looks bad):

I don't really know what to look for to make it fit better. There is an 
inbalance in trial numbers (double the amount of 0-Stimulus trials than 
any of the others) and a slight inbalance in subjects (not all tested 
all four times) - could that have something to do with it? Should I be 
looking at PQL instead of ML? Or is it the error distribution that I'm 
getting wrong?
I am grateful for any help that points me into the right direction 
because I feel like I'm missing obvious things here.
Kindest regards,
Isabella