After an asset has been purged, and later it is needed to scan the asset again, do the asset needs to be subscribed again to Qualys?
If you purge an asset you remove all data related to it, including historical data. Hence if you want to scan the asset again later, you'll need to re-add it to your subscription and you'll start with a clean sheet (no historical data can be recovered).
I would only purge a host if the host is fully decommisioned or redeployed/reinstalled with another OS or OS version. For the second case the purge will be needed to prevent having open vulnerabilities on an OS you don't use anymore, meaning Qualys cannot revalidate them, hence they'll remain open vulnerabilities in your trending reports although not applicable anymore.
There could be a number of reasons why you may decide to Purge. Generally, you would purge when you do not want the data of the asset.
When you purge an asset, it's only the data that gets deleted. The IP continues to remain in your subscription. So you don't have to add the host again.
All about purging can be found here: Purging: What, why, when, how, what happens to the data?
Retrieving data ...