The ONLY way to guarantee that your new base point will be selected every time you select an object is to save the object AND base-point as a symbol file! It will work every time! However......
When you create an object WITH a new base point and save it as a "group" you must choose that base point again to use it. This is why, in previous posts, I tell people to draw "points" (those RED temp points within the POINT tab) instead of selecting a single base point! Why?....Because you can only choose ONE base point for any object whereas you can place as many "RED temp points" as you want to create MULTIPLE snap points on any object, but you still have to select one of those points as a base point otherwise the default insertion point is the center of the object (based on rectangular boundaries). There is no way around this! By DEFAULT the center will be chosen automatically unless you choose a new location. Some would say, "then why set a base point at all if I still have to select it again to use it?....here's an easy answer....you won't be able to use it at all if you don't create it first! You will be left using the center of the object every time if you don't create an alternate base point! My recommendation is to save a base point in symbol files, and save standard RED temp points (as many as needed) in Grouped files.
When you create an object WITH a new base point and save it as a "group" you must choose that base point again to use it. This is why, in previous posts, I tell people to draw "points" (those RED temp points within the POINT tab) instead of selecting a single base point! Why?....Because you can only choose ONE base point for any object whereas you can place as many "RED temp points" as you want to create MULTIPLE snap points on any object, but you still have to select one of those points as a base point otherwise the default insertion point is the center of the object (based on rectangular boundaries). There is no way around this! By DEFAULT the center will be chosen automatically unless you choose a new location. Some would say, "then why set a base point at all if I still have to select it again to use it?....here's an easy answer....you won't be able to use it at all if you don't create it first! You will be left using the center of the object every time if you don't create an alternate base point! My recommendation is to save a base point in symbol files, and save standard RED temp points (as many as needed) in Grouped files.