This may be a bit broad of an answer as the problem description is 3rd hand. You know via another manager that has told you. There can be all sorts of team dynamics and politics that are not being surfaced via your question.
Communication seems to be a real problem. Hiding behind emails is not a way to build a highly functioning team. There sounds like things are been chucked into the "too hard bucket" that are not being discussed.
What is the progress like for the rest of the team? Are there any team feelings of being over/underwhelmed? It is best to ask this anonymously as personal dynamics and the feeling of letting the team down can affect how people react. "Everything is great! Full speed ahead off the edge of that cliff."
What sort of development cycle are you working in that the person keeps going through deadlines?
Is there also a problem with the quality of the work the person is doing? Is the team also building to a high measurable quality?
Is the person a key man risk? Are they responsible for a certain part of the system that no one else can do? Is this person having to juggle work to help others complete their tasks as they are required on so many features?
Is the person working on multiple projects at a time or just one? Is he/she working on more than one feature at a time? Are there external pressures/people that change the priorities of feature deliveries?
Multitasking is a great way to kill productivity and increase errors. It may be that his WIP (work in progress) is too high. Is the delivery split into enough slices to allow displayable progress?
Do not use percentages of progress. The feature is either done or too large to be done in a short iteration and needs to be split into separate smaller deliverable features. You do not want to get into the case of "It is 98% done all we have to do is test it now..."
Are these real commitments to external or internal customers for delivery of features or is the delivery part of some sort of Gant burn down chart? At the end of each deadline is the functionality showcased to the clients?
If we are only talking about estimations that's what they are estimations. A great way to kill team moral and encourage the wrong behaviour is to beat them to death with artificial deadlines. Once missed and the team scolded then a pattern is set. You may be dropping quality for the time constraint.