While it's annoying the alerts are easily missed, I've not found it to be a big deal if you fail to go help a settlement. You just repair whatever's broken and even if you don't do that, the items will self-repair eventually (presumably over time the settlers themselves fix it). The settlement quests can be failed in general with few consequences, although I assume if you fail them ALL the time there will be poor morale in the Minutemen. It won't break your game if you miss one though.