The behavior seems to be correct. Changes to assets/scripts are not persisted after an update.

So either the setcolor needs to be reapplied on Enable:

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

[ExecuteInEditMode]
public class Demo : MonoBehaviour
{
    private ComputeBuffer m_computeBuffer;
    public Material m_mat;

    void OnEnable()
    {
        m_computeBuffer = new ComputeBuffer(1, 16, ComputeBufferType.Constant);
        m_computeBuffer.SetData(new Vector4[]{new Vector4(1, 0, 0, 1)});
        // NEW: Copy state to temp field
        _SetColourTemp = SetColour;
    }

    public bool SetColour;

    // NEW: Use temp field
    private bool _SetColourTemp;

    // Update is called once per frame
    void Update()
    {
        Debug.Log($"SetColour {SetColour}");
        // NEW: Use temp field
        if(_SetColourTemp)
        {
            _SetColourTemp = false;
            m_mat.SetConstantBuffer("buffer", m_computeBuffer, 0, 16);
        }
    }
}

Or a new material needs to be saved (and DB needs to be informed about the changes), like:

var mat = AssetDatabase.LoadAssetAtPath<Material>( "Assets/Material.mat" );
Undo.RecordObject( mat, "Set Color" );
 mat.SetColor( "_Color", Color.red );
EditorUtility.SetDirty( mat );