It will porbably have nothing to do with SQL Server. There are many reasons for a copy job running slow, these are just a few: - Are the files/folders getting larger? - Is your network running at full capacity? - Are your disks on target or source being used heavily? - Are you copying one large file/folder or lots of small files? - Is someone else using your target/source machine and thus contending for resources?
WilliamD has some very good points. I especially would call attention to his first two bullets. But I think I can add one that is at least worth looking at. Robocopy is very often set to exclude files, for instance it may exclude those without the archive bit set (/A or /M) or else exclude older files (/XO). It could be that a large amount of data in files that were being excluded are now being included, perhaps because they are being modified more often now which will usually make them considered newer and set the archive bit.
Well, I didn't had this problem in SQL but in live server and it soon became a mess. The funny part is when I enabled its multi threaded file transfer it got even slower. I tried everything to fix it and nothing helped. Then my friend told me about GS Richcopy 360 which has 100% multi threaded file transfer. Now my problem is fixed and I am happy with its performance. Maybe you should now shift to some other software. Thanks!