Tämä lupa pysyy voimassa, kunhan noudatat sääntöjä.

Because Tämä lupa is the subject of the main clause. In Finnish, the subject of a normal statement is typically in the nominative.

• tämä = “this” (nominative singular)
• lupa = “permit/permission” (nominative singular)

pysyy (from pysyä) means “stays/remains”, emphasizing that the state continues. on (“is”) would just state a fact without highlighting continuity.

• Tämä lupa pysyy voimassa… = “This permit remains valid…” (continuing validity)
• Tämä lupa on voimassa… = “This permit is valid…” (more neutral)

voimassa is the inessive case of voima (“force/power”), literally “in force”. Finnish commonly expresses “valid” for laws/permits with this idiom:

• olla voimassa = “to be valid / in force”
• pysyä voimassa = “to remain valid / stay in force”

kunhan introduces a condition that functions like “as long as / provided that”. It often implies “that’s the only requirement” or “under the condition that.”
jos is a more general “if” and can sound more neutral or open-ended.

• kunhan noudatat sääntöjä ≈ “provided that you follow the rules” / “as long as you follow the rules”
• jos noudatat sääntöjä = “if you follow the rules” (less “requirement-like”)

Because kunhan noudatat sääntöjä is a subordinate clause following the main clause. In Finnish, a subordinate clause is normally separated with a comma:

• Main clause, subordinate clause.

noudatat is 2nd person singular present tense: “you follow/you comply with.” Finnish often omits the pronoun sinä because the verb ending already shows the person.

• (Sinä) noudatat = “(You) follow”

It comes from noudattaa (“to follow/obey/comply with”). Present tense (singular) looks like:

• minä noudatan
• sinä noudatat
• hän noudattaa

The -tt- is part of the verb’s stem pattern.

sääntöjä is partitive plural of sääntö (“rule”). With verbs like noudattaa (“to follow/observe”), the object is very often in the partitive, especially when it means following rules in general rather than one specific, completed set.
So noudatat sääntöjä is like “you follow rules / you comply with the rules (in general).”

It’s possible in some contexts, but it changes the feel. säännöt (nominative/“total object” form depending on analysis) would suggest a more bounded/complete set, like “you follow the rules (all of them, as a whole)” in a specific situation.
In everyday “rules in general / rule-compliance” contexts, sääntöjä (partitive plural) is more natural.

Finnish word order is fairly flexible, but changes emphasis. The neutral order here is:

• Tämä lupa pysyy voimassa, kunhan noudatat sääntöjä.

You can front the condition for emphasis:

• Kunhan noudatat sääntöjä, tämä lupa pysyy voimassa.
  Both are correct; the second highlights the condition first.

It can also mean “just/only (do X)” in some contexts, especially in imperatives:

• Kunhan muistat! = “Just remember!” / “As long as you remember!” (context decides)
  But in your sentence structure (…, kunhan + clause), it’s clearly the conditional “provided that” use.

lupa can mean both. In this sentence, it depends on context:

• If it’s a document/status (e.g., a license), lupa is naturally “permit/license.”
• If it’s an abstract allowance, it can be “permission.”
  The grammar stays the same either way; context tells you which English word fits best.