If your trace is giving "weak or failed" traces at the end it means that the signal at the end of the trace is too low to be improved by LongTrace. I can't really tell you much more without seeing you trace, but if you open you trace in a trace viewing program like FinchTV you can have a look at the signal at the end of the trace. You need to look at the raw data as this is what LongTrace uses to do the basecalling. If the peak signal at the end of the trace is very weak (basically flat) then LongTrace is not able to do much to improve the basecall.
A trace file is just the ab1 file that contains the sequence data peaks. I don't really know why they are called trace files - I guess there is some sort of historical reason for it.
The free service has a limit of 10 files per day - it is really only for tiny users and people wanting to try LongTrace. If you want to process more files then this you need to register for LongTrace FTP. The link to regester is here
Finally, have you tried PeakTrace too? Sometimes it is able to improve traces that can't be improved by LongTrace. The link for the free PeakTrace version is here:
Free PeakTrace Basecaller