The phrase "constant vigil" means to always be watchful and alert, paying close attention and being aware of potential dangers or problems. Full definition
For months last year, the team kept a near - constant vigil on Proxima Centauri, looking for tiny wobbles caused by the pull of an orbiting planet. (discovermagazine.com)
Once the teenager was safely ferried back to Ryder, Shatz kept constant vigil over him, operating on Sanchez six days in a row to keep the stump as clean as possible. (discovermagazine.com)
The condition can be very upsetting to owners, as it warrants constant vigil to avoid clean ups. (k9magazine.com)