[rwalle]

Not a problem?

All your previous emails are lost, aren't they? Even you have local backup of them somehow, they are not equivalent to emails saved to your server?

[edmundsauto]

Losing backups is problematic, but IMO the bigger issue is losing access. I care 10x more about emails that I haven't received yet, compared to my history. I am still not wanting to lose that history... but it is just not as big a deal.

[yumraj]

The only way to cover that case is run your own mail server.

I've done that in the past, don't recommend it unless you have a real need and know what you're doing. It wasn't hard, but just extra work that I wasn't sure was worth it.

[nephanth]

If you're using an email client, chances are you have an offline copy of your emails (depending on how you configured it)

[xuki]

If you have a local back up and the provider supports IMAP, you can just sync it back to the new provider.