If we don't build in solutions to the problem of volunteers calling off at the last minute (which I define as anything within five days of the service), it will hurt the ministry and can even lead to frustrations and burning out as a children's ministry leader. Here are some things you can do:
1. Have a back-up plan and a sub-system. You can schedule floaters/subs for every Sunday, or have them on stand-by. You could also ask a whole adult Sunday school class or small group if the group could be an "on-call group" where you could ask any of them to serve if you get in a bind. Keep in mind you would need to train and background check any subs you plan to use. Know and communicate your plan in advance.
*Don't abuse this, but you could also ask other staff members or ministry leaders (or their spouses/family members, or some of their key volunteers) if they would be willing to step in if you get in a bind, and you can repay the favor for them if they need a last minute volunteer to step in (be sure to repay the favor if you do this).
2. Have people find their own replacements. You could have a list of volunteers who can't commit to serving regularly, but would be willing to be on a sub list or on-call list, and give that list of phone numbers out to all volunteers, and ask them to find their own subs. You could use a group message feature like a group text chat, a GroupMe account, a facebook page, or any volunteer scheduling app, and let people ask others to switch with them or cover for them.
3. Overstaff your rooms and schedule floaters. When you have plenty of volunteers scheduled each week, even if some don't show up, you'll still have enough people to run the ministry. If everyone DOES show up (has this ever happened?!), the load will be spread and it will run even more smoothly. You may need to combine classes or combine small groups, but as long as you're within safe ratios of volunteers to kids, you can still run your ministry.
4. Hold them accountable. When someone calls off at the last minute, they need to know you're aware and you care. The first time it happens, you can call/email/text them and let them know you missed them. They may have a great reason for calling off or not showing up, and iit may be an opportunity to show empathy and minister to them. If it happens again, talk with them in person and ask if there's anything you can do to help them or if they can still commit to serving. If it happens again after that, be gentle but firm, and ask if serving in children's ministry is something they can still commit to, or if they want to move to a new role (maybe a sub?) or take a break.
5. Check yourself and your leadership. Are you communicating with volunteers clearly? Do they know when they are scheduled to serve/are you reminding them and asking them to confirm they are coming? Do they feel needed and valued when they're serving? Have you cast the vision for the importance of what they are doing? Are they in the right role? Is it a good experience for them when they DO show up to serve?
When volunteers know how important their presence is, and feel valued and have ownership and investment in the ministry, they are not likely to bail at the last minute. Create a culture where people want to serve, feel valued, and have ownership.