I dismount every time I go through a portal or teleport to another zone or in the same zone. I use /clearcache often and will close my game out every few hours if I play a long time to clear my windows cache. I also do the cleaning and/or relogging (close game completely) if I have spent time gathering or crafting. I have used this method for several years now and only rarely lose body parts during play.
Thanks to Maj, I've figured out not only what fixes this problem, but perhaps the cause. Since the first day I started playing I have had the setting to auto-mount activated. I like this feature a lot, but after reading what Maj wrote I first experimented with dismounting prior to every teleport, however this turned out to be annoying. Then, I recalled the setting and disabled it. I can now port and haven't had ONE issue of invisibility since I disabled that setting. I hope this helps those of you who were super annoyed with this glitch. Disable auto mount and enjoy the game just like you did before this started. Thanks Majenta!