Is there a risk of losing AAVE when staking it?

Well, first of all welcome to Aave forum! Ok so to answer your question properly, by staking your aave you receive stkaave wich is a syntetic version of your aave staked in the contract. By doing that you get an interest, and also helps securing the protocol. But, in case of a shortfall event, and always decided by governance, it may be possible to slash a % of your stkaave to help reduce the damage from a potential slashing event.