Show records that are repeated every month

You can solve it in this way with a subquery

SUBCONSULTA

SELECT cliente
    FROM compras
    WHERE cliente
    IN (
    SELECT cliente
    FROM compras
    GROUP BY cliente
    HAVING count( cliente ) >1
    )
    GROUP BY cliente
    ORDER BY cliente

What I did was

CTE

If you use mysql from version 8, you can use cliente and your query would be as follows

WITH consulta AS(
   SELECT cliente FROM compras
   GROUP BY cliente
   HAVING COUNT(cliente) > 1
)
 SELECT cliente FROM consulta WHERE cliente IN(SELECT * FROM consulta);

What I did was

  

Inside a query stored with an alias called CTE I made a consulta where I group the results provided that the SELECT   of customer is greater than 1

  

On the outside I do a conteo but not the table if not the SELECT where the CTE is in a query to the cliente query

  

Here you have a link with both examples to visualize and see if they serve you

If what you need to know is the customers who buy every month, you could start with the following analysis. For the customer to buy all months means that you must have at least one record per month (I must group per client and per month) after that know how many months I have managed (suppose 12).

SELECT cliente, count(*) -- Agrupo a nivel de cliente
FROM (
    SELECT clientes, mes_compra, count(*) -- Agrupo a nivel de cliente y sus compras por mes
    FROM COMPRAS
) AS X
HAVING count(*) = 12 -- El comparativo de los 12 meses del año

Note: The 12 months is the number established by you, depending on the months managed (in this case 12), if this value is different you must change it, if it needs to be dynamic you should support it in a subquery.

SELECT
   clientes
FROM
   compras
GROUP BY
   clientes
HAVING
   COUNT (mes_compra) =
      (SELECT COUNT(mes_compra) FROM compras)
ORDER BY
   clientes

I have not checked this answer, and may have errors.

The concept is that the subquery calculates the number of different months in the entire table. Each group also has a number of months. When they are equal, the group contains all the months, and contributes a value of clients.

It all depends ... maybe something like this will help you, you should keep in mind that the query will drop the customers who register purchases in the months burned in the where, so put only those you need

SELECT 
  CLIENTES 
FROM 
  COMPRAS 
WHERE 
  MES_COMPRA = 'ENERO' AND
  MES_COMPRA = 'FEBRERO' AND 
  MES_COMPRA = 'MARZO' AND 
  MES_COMPRA = 'ABRIL' AND 
  MES_COMPRA = 'MAYO' AND 
  MES_COMPRA = 'JUNIO' AND 
  MES_COMPRA = 'JULIO' AND 
  MES_COMPRA = 'AGOSTO' AND 
  MES_COMPRA = 'SEPTIEMBRE' AND 
  MES_COMPRA = 'OCTUBRE' AND 
  MES_COMPRA = 'NOVIEMBRE' AND 
  MES_COMPRA = 'DICIEMBRE';