I use CLC for my analysis. I have paired reads (35bp for forward and 50bp for reverse). So when I trim, the reads are bound to be below 35bp. Also in read like T131210.12, the trimming results into T131210 as '.' is an ambiguous nucleotide analogous to 'N' in base nucleotides. So if the '.' is in the beginning of the sequence, you are bound to lose lot of bp in a read. So that kind of explains why there is such heavy trimming.
And I'm using a Phred score of 17 as the limit, which I thought was alright as 70% of the sequences had a quality >=15. So you are saying that mapping with such heavy trimming could give bad results?