The too many attempts or too many requests message means several card or Apple Pay deposit attempts were made in a short window in the mobile app, and the payment system has temporarily paused further tries. It is a rate limit on the payment step.
Wait at least one hour before trying again. Depending on how many attempts were made, the cooldown can last longer. Closing and reopening the app will not reset the timer.
Trying again before the cooldown ends can reset the timer and extend the wait further.
While you wait, check that you are using a bank-issued debit card and that your billing address matches exactly what your bank has on file. Those are the two most common reasons a deposit fails before the lockout kicks in.
If you would rather not wait, you can add funds by depositing USDC. Go to Deposit, then Crypto, select the network your USDC is on, copy the deposit address, and send USDC on that same network. On Robinhood Chain the deposit asset is USDG, and the screen shows the network's minimum if it has one.