What are best practices/strategies for dealing with a team member that repeatedly ignores emails/phone calls and will not commit to new estimated completion dates on specific tasks?
When I encounter this type of resistance I first email them (cc their supervisor) and ask to set up a face to face meeting. If this is not feasible, I change the email to address both employee and supervisor and schedule a phone conversation so the three of us can work out the issue(s) preventing completion of the tasks. It goes without saying that in all thing of this nature keeping emotion out of it is critical. You can feel frustrated, but do not display this frustration to employee or supervisor. Stay professional.
Remove and replace. On a machine, if a cog is not doing its job, you would remove it and replace with a new one. A human resource is no different. This is NOT to suggest we treat people like cogs, but when you are looking at a performance capability, all resources that enable that capability--including humans--must perform to expectations.