Were all samples (files) sequenced on the same lane or in the same sequencing run? Generally, for read data obtained from Illumina sequencers, you would expect good quality in the midsection and lower quality at the ends of reads. So a quality drop in the midsection might indicate some failure (air bubbles, ...), but is not necessarily bad. You could go for further inspection of duplication levels or sequence composition (for instance using FastQC).

Please specify: 1) How deep is this drop (to what Q-score does the quality fall)? 2) Does the quality recover after this drop? I mean, does it remain low till the end of reads or it rises to normal values after the drop? 3) At what base from the beginning of reads does this drop occur? I mean, number, like 74th base