Is there any reason - other than being blocked - that I wouldn't be able to see a WhatsApp contact's "last seen" time any more?
Android users can install a 3rd party app that would allow users to hide last seen status. Apparently its a paid app.
iPhone users have the option to turn this Timestamp off in the Settings. Source.
try Secret WhatsApp
Secret WhatsApp allows you to get in WhatsApp without a trace of you! Do not ever be online. The data on your last visit will not be 'more' up to date. Simply clicking on the icon will open 'WhatsApp mode' Secret. When you close or quit WhatsApp, your messages will be sent and you will not leave a trace!
There is an app in google play to hide whatsapp status:
You must make use of " Hide Last Seen Time " feature. There are two ways to make it possible. One is Using an application and another is doing it manually. You can find complete guide here : Hide WhatsApp Last Seen Time.
There is no possible way of hiding status from your contacts on Whatsapp. Therefore if you are unable to see any messages on the status bar then chances are that the person has probably deleted his/her account or the person has blocked you. For further information regarding this you can read the FAQ section of Whatsapp. http://www.whatsapp.com/faq/en/android/23225461
Edit: it is possible for people to hide their last seen status if they are iPhone users. So Android users beware, any of your friends using iPhones can hide theirs. Its nothing they've done just to you, its a global setting for them.
WhatsApp's privacy settings allow to hide last seen. So it is possible to hide last seen without blocking the contact. But this will apply for all contacts; i.e. you can't hide last seen for specific user.