Note to moderators:
I searched the forum and it appears that this bug has not been reported. If it actually has, then feel free to delete this thread. If not, then I hope this helps. Thanks.
The Background: As you likely know, if you equip a shield, it technically stays 'equipped', regardless of whether or not you switch between one handed(right hand) or two handed weapons(including bows), meaning that when you switch from a two handed weapon back to a one handed weapon, the shield will reappear, and thus not have to be manually re-equipped. This however, is where the problem starts...
The Problem: Shield enchantments deactivate when the shield automatically reappears when the player switches from two handed weapons(including bows) to one handed weapons(right hand).
Example: You are walking through the forest. You have a shield and sword equipped. Your shield has a fire resistance enchantment and thus you are more resistant to fire. You spot a pesky dragon in the sky, so you select your bow to fire arrows at it. The dragon, now understandably furious, decides to land to breath fire at you. You switch to your sword, the shield "re-equipping" itself and you raise the shield to protect yourself from the fire. You assume that your fire resistant enchantment will protect you. It doesn't, because it is no longer active and you wouldn't know this if you hadn't checked your "active effects" in the magic menu, as your shield 'appears' to be working as normal. You have a confused expression on your face as you burn to death.
The Details: This happens regardless of whether you use the favourites menu or the regular menu to select your weapons. Despite your shield reappearing and seemingly working like normal (shield bashing, blocking etc), the enchantments will be switched off as evidenced by their absence from the "active effects" list in the magic menu, requiring you to manually re-equip the shield in order to get the enchantments back.
Temporary Solution: Manually unequipping then re-equipping your shield in the favourites menu or in the regular equipment menu will fix the problem, re-activating your shield enchantments. It can be tedious, and is not as convenient as an automatic re-equip, but it works and allows you to use the shield and its enchantments as intended.