In SSMS 2016 13.0.16000.28, connected to SQL Server 2016 SP1, if you click File, Save As, and save an execution plan, it doesn't show up in the Open Recent menu.
It's especially painful given this other bug, which requires users to save the XML query plan as a sqlplan file in order to view the graphical plan:
To reproduce it, run this query:
SELECT * FROM sys.databases
st.text AS QueryText,
qp.query_plan AS QueryPlan
FROM sys.dm_exec_cached_plans AS cp
CROSS APPLY sys.dm_exec_query_plan(cp.plan_handle) AS qp
CROSS APPLY sys.dm_exec_sql_text(cp.plan_handle) AS st
Click on the query plan. It shows up as an XML document rather than a graphical plan (that problem is bug 3113287). Click File, Save As, and name it as "my beautiful plan.sqlplan" so that you can view it graphically later. Close it.
Then click File, Open Recent, and "my beautiful plan.sqlplan" isn't in the recent files list - even though it was just saved.