I had this same problem with my 2012 3005 last year during the summer. I was going nuts. I finally started blowing air through the fuel line back up into the tank and after about a month of fooling with this the problem seemed to Disappear. I ran all the fuel out so I could see into the tank, but found nothing.
Now, a summer later, I am starting to have the same problem. I pulled the fuel line and had incredible flow, almost like a garden hose with a high pressure stream. Yesterday while mowing I was still having the problem and loosened the gas cap. I did have a an improved ability to mow, but still had the tractor dying about every 20 minutes.
Last season, I was getting no fuel through the line and thinking that possibly the fuel line had deteriorated and a small piece of rubber was occasionally flipping down and blocking the fuel from getting through the hose line. When I would blow air back up the line, it would fall back up into place, then later as the fuel went through the line, flipped back down and blocked the flow again. I haven't replaced the line, but plan to along with looking at the fuel cap and running fuel back out again to check for debris in the tank again. Seems like the summer months are creating a problem though.