The phrase "constant upkeep" means the continuous effort or maintenance required to keep something in good condition and functioning properly. Full definition
Humidifiers require constant upkeep, including cleaning it and regularly changing the filter or demineralization cartridge, if applicable. (momtricks.com)
Many companies have a website that is integral to their business, and that website needs constant upkeep in order to remain relevant and bring in business. (monster.com)