SQL Server cluster not available after failure of the "main" server
Without looking at the cluster logs or any other form of error reporting, all I can do is guess here.

But my initial thoughts are that you may have hit the failover threshold.  By default, this is going to be set to a maximum of n - 1 failures (where n is the number of nodes) over a period of 6 hours.  Yes, that's a long time, and especially in a 2-node cluster that isn't very many failures (only equates to one failure).  This threshold is set to prevent the Ping-Pong effect of cluster groups.

In production, this is probably a good thing.  But in testing/development/non-prod it is pretty common to run into this initially perplexing problem, as you may be trying to consecutively failover.  It is worth noting that these parameters are 100% configurable.  All you need to do is go into the properties of the cluster group, and in the "failover" tab you will have the option to change these two parameters (Maximum failures in the specified period and Period (hours).  Here is what this looks like in the Failover Cluster Manager:



Note: in my screenshot, the threshold is set to 2 because I have a 3-node cluster.

Likewise, this can be seen with PowerShell (accessing the FailoverClusters module).

# you may need to set your cluster group name to whatever it is named
# in your environment
#
Get-ClusterGroup -Name "SQL Server (MSSQLSERVER)" | 
    Select-Object Name, FailoverThreshold, FailoverPeriod