Can we keep PI AF server 2015 and PI Data Archive 2017 R2 in our PI system.
Yes you can, though there are many advantages to upgrading AF to a more recent version, such as improvements in Analytics, analysis recalculation (manual in 2016 R2, and automatic recalculation was introduced in AF 2017 R2), and integrated AF Notifications (AF 2016 R2).
What is the reason for not wanting to upgrade AF? As John mentioned there a lot of functionalities that were added in the later versions.
I found below from the release note of PI Data Archive 2017 R2
PI Data Archive Requirements
This version of PI Data Archive requires PI AF Server 2010 R3 (188.8.131.5231) or greater at installation time. This requirement is new to PI Data Archive 2016 or later, previously the minimum version requirement was PI AF Server 2010.
As per above, minimum requirement is to have PI AF Server 2010.
What's preventing you from upgrading your AF Server?
Can you? Yes
Should you? Maybe, probably not.
What is the reason behind upgrading PI Data Archive and not AF?
Retrieving data ...