I'm not entirely confident that this will prove to be the answer but ...
Way back when beta testing V7 I had an incident where a model seemed to give very odd results extremely similar the the events you describe. Never found anything. A year or so ago someone else reported a very similar problem and I saw another instance. In both cases re-creating the model seemed to fix the problem. I think what had happened was that somehow the model file had become corrupt and the internal structure of its components was giving odd and unpredictable results. In fact I saw some very odd looking stuff when attempting to look into one of the problem files with an editor. I felt there was no way it could be recovered - or at least not recovered quicker than creating a new model.
The other possibility might be that there is another slightly different version of the model file around and sometime you get that one instead. Especially possible if you are sometimes running the thing manually to check the process and sometimes using the automated version. But if you can discount that possibility then I would favour recreating the model in case the original has been corrupted my something.
I'm not sure I can help with your second problem excpet to say I suppose it is possible that that also is due to some sort of file corruption, perhaps in the Project file if you are using Project Exports.
Not sure if the Model and Project information option would make things visible - I don't relish the idea of try to corrupt a file to to find out!
I hope this suggests something that might lead you to a solution.
Thanks for the help I'll rebuild it now.
Another probelm that may need the same solution is the JOINS in two of my models keep dropping in the automation. It ran for months and now it says the join does not exist (?)when I go in it is missing part of the path. (?) Very strange, but rebuilding make a lot of sense.