It sounds as if your dog has a condition known as paraphimosis with partial phimosis. I will briefly explain as follows:
Paraphimosis is protrusion of the penis, with an inability to retract the penis back into the prepuce, due to a constriction of the prepuce behind the glans (glands) part of the penis. In this particular case the paraphimosis is actually due to a partial phimosis that prevents retraction of the swollen glans (glands).
The causes for paraphimosis in the dog include a small preputial oriface, shortened prepuce, weakened preputial muscles (or other abnormality of the preputial muscles), trauma to that area, or idiopathic, which means that they have no known cause.
Phimosis refers to narrowing of the orifice of the prepuce. The condition may be congenital, In congenital phimosis, the preputial orifice may be so small.
In other words, once the tip of the penis comes out, the sheath is too tight to allow the penial tip back in easily, and too short to cover it, and/or the muscles in the sheath are not strong enough to hold the penial tip back in.
Unfortunately, surgery may be the only definitive or permanent option, since it is probably a congential abnormality. To my knowledge I do not believe that neutering could have caused the problem, unless there is a hormonal component to the problem, of which I am unaware. The neutering surgery is performed on the testicles, which are far away from the penis so there is no chance of mechanical injury during the surgery. Surgical correction of the penial defect is not a difficult procedure, if performed by the right surgeon, but may be necessary to prevent necrosis of the tip of the penis. Prior to surgery the tip should be kept lubricated, and you can mechanically put the penis back in the sheath but it will probably just keep coming out. And sorry, I do not know of any dietary change, or supplement that will help. Only your veterinarian can assess how serious this problem is. If your vet believes that there is little chance of necrosis, or trauma (whether self inflicted by your dog licking, or the tip being scratched on a sharp stick, for example), than the problem may not require surgery.
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