Ok. Don't know why your reminders would be disappearing. But no, the Reminders app does not sync with the Calendar app in any way. The only thing I can suggest is the usual fixes, if you have not already tried them.
Oh, and you could try turning off Reminders in Settings > iCloud and then turning them back on. That might fix any sync problems that have cropped up. Be sure to check them out at icloud.com from a computer browser first, to make sure they are being synced in the first place.
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The usual fixes:
When you have problems with an app it's a good idea to clear it from RAM.
Close/Clear the app: With the problem app closed, double tap on the Home button to get the multitask bar. Tap and hold on any icon in the bar until they jiggle, then tap the minus sign on the problem app. This will remove it from RAM and insure a clean start the next time you launch the app.
If that does not work try a restart,
Restart: Hold down the power button until the power off slider appears. Slide it off. When the iPad finishes shutting down, hold down the power button again until the Apple logo appears. Apple recommends you restart the iPad at least once a month.
and then a reset if that does not work.
Reset: Hold down the power and home buttons until the Apple logo appears. The iPad will reboot. This usually takes a bit longer than a restart. takes a bit longer than a restart.
Reset All Settings: Another, somewhat more drastic thing you can do is Reset All Settings. You'll find this under Settings > General > Reset > Reset All Settings. It won't erase any of your content, apps, or accounts; but you will have to go through most of your other settings and re-tweak them back to your liking.