Try as Jens suggests first.
The Stock PSU should be able to handle that but it is aging of course so in the long term recapping or replacement might be a good idea.
I had similar issues to you with my old Subway USB, using en external powered USB Hub solved them. But power is not enough on the Clockport hence the RapidRoad taking power from the floppy connector on A1200/A600.
Check with Jens or the Manual to see if you can also use the external power from a floppy connector within your A4000.