If you are talking about blockchain.info wallet it's probably an issue with their site or database. Contact their support: https://blockchain.zendesk.com/home
On the actual block chain itself it is not possible to delete transactions.
If you are talking about deleting transactions (history), it is not possible, as it is one of the factors that make the blockchain secure, so it is not possible.
I do not recommend using the same wallet for using faucet for a long time, especially for light weight ones, because they will easily lag on loading them.
BTW I'm still using my blockchain wallet with no issues.