Dear Isabel
Thank you for your post and for joining the forum.
I have carefully checked your output files and can confirm that nothing is wrong with the estimation. The differences may look large, but they are small when taking the uncertainties in the estimation into account. I'll explain.
Fit statistics are computed from plausible values. Plausible values are random draws and will be different every time ConQuest estimates the model. The degree of variation between different runs depends on the size of the measurement error. Measurement errors are larger for smaller samples and for models without regressors. While the standard number of plausible values for case estimates is 5, only one value is drawn to compute fit statistics. Therefore, if the errors are large, the difference in fit statistics may appear to vary between runs. However, if you look at the t-values of the fit statistics, the conclusion stays usually the same. For example, if you look at your first item, the weighted fit appears quite large in the 2007 and the 2012A versions (larger than 1.2) and smaller (1.13) in the 2012B version (it actually is the Nov 2015 version), but when you look at the t-values you'll see they are all smaller than 2 and therefore not significantly different from a value of 1.
You can decrease the fluctuation for small samples by increasing the fit draws (set fitdraws=n;). The default for n is 1. You could use 5 for n or even 10.
I hope this answers your question. Please let us know if you have any further queries.
Eveline