At first glance, two possibilities: 1) you did not properly delete the old address and it is still there or 2) the old address is still in some resolver's caches for the duration of the record's TTL (Time To Live). Because of the symptoms you describe (sometimes, ping displays the new address and sometimes the second, and I assume you ran ping on the same machine), I would vote for 1).
Hard to say more since you did not provide details, especially the real domain name. https://dougbarton.us/DNS/bind-users-FAQ.html#RealNames
You can see which hypothesis is the right one with the dig command on Unix. For instance, with www.example.com :
% dig AAAA www.example.com
www.example.com. 170199 IN AAAA 2001:500:88:200::10
Only one IP address here. If you see two (by the way, AAAA = IPv6 address, A = old IPv4 address), it means hypothesis 1) is right. Otherwise, check the number in the second field. Here, 170199 seconds: the address record will stay in the cache for a bit less than two days. Retry dig and you will see this time-to-live decrease.