If you are a website developer or programmer and look after client’s websites or apps, then you need to ensure that they are updated on a regular basis to ensure that they are secure. If you built the site using WordPress then you may need to update WordPress and any plugins that you use. If you have added in any of your own code then you should also ensure that it is up to date and secure.
Often business owners or developers are not aware that there is an issue until their hack becomes compromised. This may mean that someone can hack into the site and add / remove content or even access private information that is on there. If this happens and you have not maintained the site you could find yourself liable for damages.
Your client may not be aware of the importance of keeping the site updated in terms of security. It is recommended that you contact them and suggest that they allow you to carry out the changes that are needed. There is no reason why you cannot charge them for this unless you have agreed to do updates within another fee you have charged them previously.