Is it permissible to touch a dog for training, and is it true that touching a dog invalidates prayers for forty days?

We have found no evidence indicating that one who touches a dog will not have their prayers accepted for forty days. This might be a fabricated (Mawdu‘) hadith, because keeping a dog is permissible for certain purposes, and it is inconceivable that such a severe threat would be issued concerning a permissible matter. Even if the hadith were authentic, the non-acceptance of prayer does not permit abandoning it, because performing it absolves one's responsibility (dhimmah), even if no reward is obtained. Thus, non-acceptance here means the non-receipt of reward, not the non-fulfillment of the obligation. Keeping a dog for guarding is permissible, and touching it is permissible out of necessity, and it is recommended to have a dedicated garment when touching it.