What happens is your Trezor gives xpub to myTrezor web wallet and the wallet asks backend BoP server for all your transactions. The one you don't see is missing in the list provided by BoP. It is clearly there when visible both on blockchain.info and on btcreceive. I assume there is some glitch in BoP, which is unfortunate, but there are three things that can happen:
1. Issue fixes itself when BoP is restarted.
2. BoP developer fixes the issue if you report it to satoshi labs.
3. BoP will find your transaction without doing anything. Have you tried "Forget device" and replug?

Concerning "recovering" the BTC: If you had more choices of wallet software then you could use any of those and there is high probability you would not see the same glitch you see now. If myTrezor does not see the transaction then Electrum probably would, because it uses completely different stack. You should not be worried about your funds, because you can always recover them using other software that is being developed and will be here soon. But there is some risk you will be blocked and need to wait until the bug is fixed infrastructure is there.

Note: This is an if situation.

In the unlikely event that my Trezor breaks and I also lose my recovery seed what can I do? Is there memory on the Trezor that I could somehow extract to get my coins back or something?

If "Trezor breaks" than this usually means one of it's components does not work. If you manage to break it, the first thing that stops working is probably just display, next thing is board and only then MCU breaks. If your Trezor is broken, there is a chance MCU is still fine. If so, it can be reconnected to a new board and used (but this needs some nontrivial technical skills).
If buldozer runs over you Trezor and MCU is broken, you need your recovery seed.

The BoP can't see it because it  follows BIP0039 standard where the gap limit is set to 20, see https://github.com/bitcoin/bips/blob/master/bip-0044.mediawiki#address-gap-limit

What happens is that 3rd party wallet are not BIP0039 compliant in this detail, which cause confusion in compliant wallets like myTrezor. The remedy is as follows: fill the gap limit with several small transactions, so that the difference in path of two transactions in the account is always less then 20.

In this case we have payment on the address 44. It should be enough to send 0.001 BTC to address number 15 and 30.

So here is an update on my situation. I checked mytrezor again this morning and the balance is now correct and the transaction in question is now showing up in the transaction list. I'm guessing the bop server needed a little time to refresh?
 
I kinda wanted to put this scenario to the test to see what would happen. Now I know.

I have seen this happening to some customer and is temporary for the connection. You will see it confirmed once you close the myTREZOR browser window and reopen it after a delay sufficient (I think about a minute) to drop connections.

Hi,

I noticed the strange thing.

The Trezor is device for signing all outputs and all outputs should be showed to me in screen and values of each output.
Is it correct?

But i noticed that when i send some money to addresses A, B, C (i did the transaction for 10 addresses) there was 11th output - it's OK, one address is change from my wallet.

BUT! The 11th address is not showed by Trezor (or 1st) - this is the change adress. So one address slips away from my eye. It's very strange.
How the Trezor decides that one address should not be showed (and value too!) to me when i sign the transaction?

I understood that it made may be for easy using. But i would know the algorithm for this decision.
May be there security hole? Can hacker tell to the Trezor that one X address from faked transaction is change address and after this the Trezor could not show to me this address and value in Trezor's screen?

I can imagine that the Trezor could get the change address as path of BIP32/BIP44 and inside itself can recalculate the address and after it decides that this address is a really my own change address and doesn't show one me and value for it. But i am not sure that this done same way. If there in protocol only bit for address (change/not_change) - it will be security hole for trojan.

I think the Trezor should show all outputs and value of each output included a change address. A change address could be showed with remark 'Your Change' or other way. Otherwise, the thought creeps in that the algorithm has a loophole.

How do you think?
And what does Stick or Slush think about this? I don't want to ask this to through ticket system because the Trezor project should be discussed publicly.

If you have less than $1000 in BTC then this product may not be for you.  But for someone who has thousands, tens of thousands, hundreds of thousands, etc. then this is a great product.  I love this little thing.  I have 5 of them and will be ordering a couple more for Christmas gifts for people I know that have BTC holdings.  It is the second best thing I have ever purchased with BTC, the best one being a case of Girl Scout thin mint cookies.

Stop
It can be calculated based by blockchain.
Trezor doesn't know the blockchain. So it cannot calculate it.
Only computer with opened site MyTrezor.com can help because only computer knows which addresses are not used.

Sorry if this sounds mean but I don't think you understand how bitcoin works. I can give you some great links if you like that will help you understand on a more technical level.