It's hard to be certain, but it looks like it might have a mildew infection. Try spraying with a fungicide or Rose Clear.

I wouldn't say furry blobs snoop, more like a milky coating. As if they have been covered in talcum powder.

I would suspect Mildew as well..

Dear old Zephers is known for mildew. It is its only failing as it is a beautiful rose.
If possible, keep it on a north-facing site. This will reduce the amount.
If it is to big to move, spray it with rose-clear regularly. It won't get rid of it but will reduce it.