I have a 2001 Softail and lately there are times when I roll on the throttle I get a delay in power and it sounds like it is sucking in air?

 

Might be an intake leak. Start it up and spray some WD40 around the area where the intake manifold mates up to the heads on both sides and see if rpm changes or if the engine stumbles.

Might be a leaky head gasket. Do a compression test.

 

Hose going to voes switch/fuel shut off is a likely culprit also.

 

01 softail has map senor on intake, and no voes. Does have a vacume line running to fuel shut off, but a leak would keep it from running.

 

I would look at the manifold, just had a similar situation on my 96 softail and after examining the manifold noticed a small crack.