Generally, the subjunctive is not used with "saber," whether it's present tense ("No sé si puedo jugar") or past tense ("No sabía si iba a poder jugar"). Before I say more about that, let's first review what the subjunctive does and in what situations it's appropriate. Wikipedia in English says:
The subjunctive is a grammatical mood (that is, a way of speaking that allows people to express their attitude toward what they are saying) found in many languages. Subjunctive forms of verbs are typically used to express various states of unreality such as wish, emotion, possibility, judgment, opinion, obligation, or action that have not yet occurred.
Subjunctives occur most often, although not exclusively, in subordinate clauses, particularly that-clauses. Examples of the subjunctive in English are found in the sentences "I suggest that you be careful" and "It is important that she stay by your side." (The corresponding indicative forms of the verbs in bold would be are and stays.)
Wikipedia in Spanish says:
Toma el carácter subjetivo de posible, probable, hipotética, creída, deseada, temida o necesaria.
With "saber," the subjunctive would sound pompous to my ear.
If there is uncertainty, doubt or disbelief, such as "No creo que llueva," "No creo que vaya a llover," "Dudo que llueva," etc., then the subjunctive is used. Also, the famous connecting "que" mentioned in Wikipedia clues us in that the subjunctive will probably be a good fit.
In "No sé si puedo ir" and "No sé si va a llover," I will either be able to go or I won't be able to go; it will rain or it won't. I don't know yet what's behind Door #2.