Thank you for your answer Craig, but, fortunately, I maage to find the problem.
When I've done all those tests on Friday I forgot to check the SCORM file itself, I was sure that working fine for such a long time (around 800 learners completed that course since it's in program) there could not be any problem with it. But you mentioning the SCORM opened my eyes.
The problem was with the setting in the scormdriver.js
var SCORE_CAN_ONLY_IMPROVE was set to FALSE and var REVIEW_MODE_IS_READ_ONLY was set to TRUE.
Probably at his first attempt the learner did not get the score for one of the SCORM questions at some point or did any other mistake but, because only the first time you finished the course was taken into consideration, no matter how many times he tried after, the course kept only the records made first time and showed the course as incomplete.
After correcting the variables and replacing the old SCORM with the modified one in the course, the next time I tested it on the learner account the new values obtained at the end were recorded and course showed completed.
Thanks,
Andrei