Playing

I work in a customer- or patient-facing role and just can't get up to answer the phone when it rings. After a round of phone tag, I left a voicemail, stating, Tag, you're it... " it seems like we're playing phone tag. Can you email me at _________? And we can set up a time to talk? Did that hurt my chance? I can't be readily available every single moment, but I want to be respectful to my current employer.