All things being equal, you should always install a device's updates as soon as possible. For Apple iPad 2 owners, all things are not equal.
The latest iOS 9.3 update, which carries both system improvements and important security fixes, stands a very real chance of completely bricking second-generation iPads. At present, there's no word from Apple on what to do, or a surefire solution for iPad 2 users. For now, the best option may be to leave your device unpatched — which could also leave it open to attacks.
The Apple Support Communities forum runneth over with disgruntled users for whom the iOS 9.3 update left their iPad 2s in a state of perpetual-update limbo. After the update completes installation, the device is unable to activate — it won't connect with Apple's authorization servers. Since activation is a vital step to do anything on an iPad 2, the older device has become a large, expensive paperweight for a great deal of Apple users.
At present, it's hard to tell how prevalent this issue is (users whose updates worked perfectly have no need to post about it, after all), but at the very least, there does not appear to be any way to predict which devices will get stuck.
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It would be easy enough to skip the update if iOS 9.3 were simply aesthetic, but it's not. Apple has taken the opportunity to load almost 30 security fixes into the patch. The flaws being fixed are not all catastrophic, and Apple has not released the exact details of how each works. But a clever hacker could probably reverse-engineer them and start targeting iPad 2s. After all, there's a good chance that the machines are unprotected.
For users whose iPad 2s have been rendered useless, there is yet hope. Some users have reported successful activation by hooking up their tablets to computers and running iTunes. If you have Find My iPhone activated, remove your iPad from the service. Then, plug your iPad into your computer and run iTunes. With any luck, the software will download the latest update for the tablet and push it through the activation stage. This is not an absolute method of success, but it appears to have worked for the majority of users.
Apple has addressed this issue, for the time being, by providing some potential workarounds for iPad 2 owners in distress. In the meantime, you may want to turn your iPad 2 off and leave the update for another day, unless you really need it in the interim. If you can't live without it, either update or don't — either way is a roll of the dice.