Again, I was too fast on the trigger.
When comparing the shortcodes for different plans, I realized I had been using the wrong pro-forms (recurring form) instead of the buy-now pro-form.
Even though I had selected XX $ for 1 day non-recurring it gave members access to 1 month..
I have redone my pro-forms with Buy-now, instead of recurring (with non-recurring option)
The shortcode now looks like this:
[s2Member-Pro-PayPal-Form level="1" ccaps="" desc="Uden abonnement / 12,- for 24 timer" ps="XXXX" lc="" cc="DKK" dg="0" ns="1" custom="www.XXXXX.dk" ta="0" tp="0" tt="D" ra="12" rp="1" rt="D" rr="BN" rrt="" rra="2" accept="paypal" accept_via_paypal="paypal,visa,mastercard,amex,discover,maestro" coupon="" accept_coupons="0" default_country_code="DK" captcha="0" /]
I hope this solves it, but please confirm it :)