Since this request is for historical data of the artifact we will have to use the Lookback API.
Here is an example
Lookback API query you can use:
https://rally1.rallydev.com/analytics/v2.0/service/rally/workspace/
<<Workspace Object ID>>/artifact/snapshot/query.js?find={$and: [{"FormattedID":
<<Artifact FormattedID>>}, {"Blocked": true}, {"_PreviousValues.Blocked": false}]}&fields=["_SnapshotDate","_SnapshotNumber","Blocked","Blocker","BlockedReason"]
This query is requesting all snapshots of the artifact where the
Blocked state was '
true' along with a
_PreviousValue of the
Blocked state be '
false'. This combination suggests this was a snapshot where the artifact was set to be blocked.
Here is a screenshot of the
JSON output:
<Please see attached file for image>

In above JSON you see this artifact was blocked 3 times in snapshotNumbers 1, 5 and 10. You can see the timestamp of each block and the user (objectID) who blocked it.
Note:The
BlockedReason field might not necessarily conform to the same snapshots of the
Blocked state. Reason may or may not have been given, and unnecessarily in the same snapshots. Therefore, if you needed to make certain of the
BlockedReason that correspond to
Block, you may need to run subsequent queries to find the change in the
BlockedReason field subsequent to each of these snapshots.