... and the LORD be with thee, as he hath been with my father. (1
Samuel 20:13b, KJV)
Looking at the Hebrew underlying this sentence it appears that the "has been" translation is more accurate. Saying "used to be" actually narrows the scope of interpretation, essentially giving the translators' interpretation while removing other possible interpretations. "Has been" could mean either that God used to be with Saul or that God continues to be with Saul. And the Hebrew verbs are often ambiguous with respect to time.
Here is that sentence in the interlinear, showing grammatical notations for the Hebrew.

The verb at the start of the sentence is the same verb later translated as "has been," but notice that it is in a different shape.
First Occurrence
The first occurrence of H1961 is joined to the "and" conjunction, as is typical of weqatal and wayyiqtol verbs; and this verb is said to be a Qal (simple) verb in the imperfect jussive state. A jussive verb is technically a command, but it is well understood in Hebrew that one does not command God, so this becomes more like a blessing or a wish/desire in this context.
Second Occurrence (That of the Question)
The second occurrence of H1961 is given in perfect form, and lacks the conjunction. In modern English, a perfect verb must always have the verb "to have" as a part of its conjugation. (I say "modern" because older English could use "to be" within the same context, e.g. "The Lord is come" instead of "The Lord has come".)
The translation of "used to be" has exchanged a perfect tense verb for one that is a modal infinitive. I would submit that this is difficult to justify, given the Hebrew.
Conclusion
The "has been" translation appears superior to that of "used to be" in 1 Samuel 20:13.