Regardless of what the problem is, the solution is always the same. It requires a computer with iTunes attached to your iPad or iPhone.
Access via iTunes
Use Apps -> File Sharing and you'll see the MIDI Designer icon of the app that won't start.

Before You Start
Drag all of the file under "MIDI Designer Documents" to a folder on your computer to back them up.
Solutions
Easiest, try this first:
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rename autosave.mididesigner to was-autosave.mididesigner
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delete autosave-preset.xml
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delete config.xml
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try restarting
If that doesn't work, delete the app and download it again from the App store.
If your layout is causing the App to crash (e.g., you perform load layout and the App crashes) get in touch via Config -> Actions -> Email us. We can probably recover your layout.