Consistency Issue

I apologize if this is an easy issue to resolve but I am very new to using a laser and I am having an issue. I am using our laser to cut out rectangles with people’s names on them. (Kinda like a name tag but smaller) Everything was operating normally and I noticed some of the lines started to deviate. Several times when making multiple passes, the lines would not match up. I tried to redo these and the same issue keeps happening. The names now look almost fuzzy and i don’t know if that is a laser focus issue or number of lines issue. I decided to make a test cut in a straight line. Everything looks good except for the last inch. When the machine travels Y-, the laser will dip down roughly .5 mm and X+ 1mm. At the end of the cut, it returns to the correct position and moves Y+. It will do this every pass. Can someone point me in the correct direction because I feel lost and hopeless?