"Siempre hay una próxima vez."
Translation:There is always a next time.
Both are correct. They apparently just decided to put "siempre hay" this time. But word order is really flexible in Spanish, as long as the objects follow the verb in a sentence (or precede in it in the case of pronouns) you can put the adverbs wherever. "Mi madre siempre me grita" or "Siempre mi madre me grita" or "Mi madre me grita siempre" all have the same basic meaning, just a slight difference in emphasis. Interestingly, "hay" can take a direct object. "¿Hay mujeres lindas allá? –Sí, las hay."
I would say "There's always a next time".
However, sometimes it is difficult to know where Standard English ends and dialect begins. We should just go with whatever sounds best. I don't believe any of the suggested versions are likely to be easily misunderstood.
In any case, I would probably only use the phrase ironically because often it isn't true. There is another saying: "It's never the same twice"! :-)