Ein Problem kann plötzlich wieder auftreten.

can

Breakdown of Ein Problem kann plötzlich wieder auftreten.

• plötzlich: suddenly
• wieder: again
• das Problem: the problem

Questions & Answers about Ein Problem kann plötzlich wieder auftreten.

Why is Ein Problem in the nominative case with an indefinite article, and not Das Problem?

Because Ein Problem is the grammatical subject here and you’re speaking about any problem in general, not a specific one. In German, the subject takes the nominative case. Das Problem would be definite (“the problem”), while ein Problem is indefinite (“a problem”).

Why is kann in second position, and auftreten at the very end of the sentence?

This follows the rule for main clauses with a modal verb: the finite verb (kann) goes in the second position, and the main verb in its infinitive form (auftreten) is pushed to the end.

What kind of verb is auftreten, and why isn’t the prefix auf- split off and placed at the end?

auftreten is a separable-prefix verb (auf·treten). When used with a modal (here kann), you keep the full infinitive together at the end. Without a modal, you would separate it:
• Ein Problem tritt plötzlich wieder auf.

What parts of speech are plötzlich and wieder, and why are they placed between kann and auftreten?

Both plötzlich (suddenly) and wieder (again) are adverbs modifying auftreten. In German, adverbs normally follow the finite verb, so after kann you can list one or more adverbs before the final infinitive.