Standard Error and model convergence

[vankatwy]

I have a suspiciously small SE for my population estimate. To test if I had a model convergence issue I reduced the number of trapping occasions used from 6 (i.e. 100101) down to 3 occasions (i.e. 101). My logic is that if the SE indicated it was a poor estimate at 6 occasions it should get more unrealistic (i.e. SE=0.0000001) at 3 occasions (see below for the N-hat and SE from each # of occasions). Since the SE gets larger with a reduction of occasions I am inclined to think the estimate with 6 occasions is valid.
Is anyone else similarly convinced or is my logic flawed?
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Occasions N-hat (SE)
6.............39.000000(0.000454)
5.............39.000855(0.077156)
4.............39.200648(0.853932)
3.............38.085067(2.195309)
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Any comments are greatly appreciated!
Cheers,
Kristin