Not sure what you mean by 'register the block height of a transaction', but the likelihood of a block being orphaned becomes exponentially more improbable the deeper it is in the chain.
I mean I was doing some calculation on the following transaction taking it as a reference.
https://blockchain.info/rawtx/114f37f3e30c7d9b5d5339e9a1652f2f065d0413fe34ee1121de0f21a50aaed3As far as I can remember, the block height I registered for this transaction was 273824. But now it seems, its block height is 266559 !!! So, I am confused, if it is my mistake or block height can change with time !!!