Well, you just tell them the truth. Software development is not something that (usually) is very well plannable, as we are always doing new things, and need to experiment. That's why estimates do not always work, and urgent questions cannot always be handled rapidly. Be transparent.

When delays happen in urgent requests, I believe it’s best to be open and upfront. I inform the client early, explain the reason for the delay in simple terms, and provide a realistic new timeline. I also outline the steps I’m taking to get back on track, which helps maintain trust and shows my commitment to delivering quality work.

For most cases I’ve found these tricky situations can be avoided by managing expectations with clients early and often. For programming, it’s also about breaking down work into small tasks so that each task can be escalated when needed. This requires getting access to the right stakeholders at the right time and communicating issues and trade-offs often. In situations where unexpected delays still occur, the same principles above apply but it’s about getting more support to understand and articulate the issues and making decisions on priorities. Maintaining trust is not only being an expert in your field but being honest. This includes highlighting areas where you’ll need more support.

Transparency is key to building trust with clients. In case of delays, it's essential to communicate openly. I would inform the client about the reason for the delay, ensure they understand the situation, and provide a realistic deadline for delivery. This approach not only manages expectations but also strengthens client relationships in the long run.

Delays have many a times, justified reasons. And, these reasons can be shared with the clients. The reasons may be to introduce certain security provisions, making the program more robust, to incorporate recently discovered vulnerability in the market, adding better maintainability, and so on. You can easily convince the client that these delays will help your product better, robust, maintainable, etc. And these are with no additional cost. The client will be easily convinced.