Are you talking about a google app for contacts or the phone's contacts app? They aren't the same. The app that comes with the phone should work with your google account. You just have to sync the contacts to your account.
Using Gmail Contacts on my desktop synced with phone (Android) contacts app.
Over the last year or so, like many others have complained about, I've had critical contacts just disappear several times - on phone and/or computer. I don't have confidence in Contacts any more, but want to continue using Gmail.
Alas, the problem is likely not the contacts app that came with the phone. It could be a flaw in the phone's system itself. Depending on what OS it is and what preinstalled things the carrier/service provider and the manufacturer have put on it. However, I can't recommend any specific other one.
I have to say, other than a flaw through what I mentioned above, issues on google's end or user error, I have not seen any major issues with the standard contact apps. Even in the newer versions of Android.