Can I keep contributing fresh money to my NRE account from my US salary, and are there limits?

Yes. The entire purpose of an NRE account is to hold foreign earnings you remit into India, so you can transfer money from your US bank to your NRE account as often and in whatever amounts you like, subject only to your US bank's outward-transfer limits and any anti-money-laundering documentation. There is no India-side cap on inbound remittances into NRE. The balance and its interest remain fully repatriable. Keep records of each transfer showing the funds came from your US after-tax income, which helps if you ever need to prove the source for repatriation. Note the account and its interest still count toward US FBAR and Form 8938 reporting once your combined foreign balances cross the thresholds.