Usually this type of problem is due to low transmission fluid or a low fluid pressure internally of the transmission. Slow to reverse is usually a pretty common symptom of early transmission wear and the need for an overhaul.
I would talk with the transmission shop and get them to experience the problem. Personally I would go ahead and service the transmission fluid and filter and see if that helps the problem. Normally I would not recommend you do this in this situation since it can sometimes cause the problem to get worse, I think I would take a chance.
Since you did not mention anything about the transmission slipping in any of the other gears...again, I would change the fluid and filter. I would also use a transmission fluid additive designed to prevent slipping after the filter has been changed. Most transmission shops will have a favorite brand in stock.
There is a chance this could be a linkage adjustment issue, so make sure the transmission shop checks the linkages and bushings to rule out a possible out of adjustment issue.



