(1) I once sent a group of poems to the Amherst Review. I waited a year to get a response. Finally, almost one year to the day after I sent them, I got a letter saying they wanted to publish one of the poems. I sent them the writer's info and waited again. One year later the issue with my poem was published.
They had left out a word.
(2) The only sure way to get published is to outlast the rejection slips.
(3) The times they are a changin.
Typically, when you send a poem to a literary journal, you can expect to wait anywhere from 6 weeks to 6 months to get a response. Ideally you can use that time to get your mind off the work you just sent out and turn to other work that needs to be completed and sent out. Then when the to-be-expected rejection letter comes, it's no big deal, because you've already moved on to other things that have assumed greater priority. That let's you get reacquainted with the work that came back. You can look at it objectively and analyze it to determine whether you need to trash it, revise it, or simply find a better match to send it to.
But now we use the Internet to submit our work. Some journals still take three months to decide to tell you no. But one day last week, I got a rejection email 12 hours after I had sent the poems.