My first epidural did not do anything for my pain. Should I try it again with this child?

Yes. Infrequently, epidurals are not effective due to a number of factors. Nonetheless, they are an excellent analgesic for labor pain, beneficial to both the mother and your soon to be born baby. I would strongly encourage you to have an epidural placed by a qualified anesthesia provider for your next delivery. Good luck!
Yes. Sometimes epidurals do not work well. The timing of the placement and the skill of the physician play a role. Just because it failed before has no bearing on what will happen this time. Good luck and congrafuulstiobs.
Depends. If you have high pain tolerance and quick delivery then you may not want it. If however you were uncomfortable then your lack of relief may simply reflect poor placement. Usually great pain relief is obtained if placed early in labor. If already fully dilated and ready to deliver consider intrathecal fentanyl. Ask the anesthesiologist to speak with you early in delivery.
If you need it. Sometimes a second labor and delivery will progress more quickly and you won't need an epidural. If labor is slow and painful, ask for an epidural. The success rate isn't 100%, but the chances are you will get some pain relief. Sometimes it is harder to get good pain relief if labor is most severe in the lower back, which can be different between one pregnancy and the next. Good luck!
Epidural for Labor. Effective epidural depends both on placement and timing. Needs to be placed before late stage of labor when all pain is located low and typically patient feels like they are having painful bowel movement. Best if placed in earlier labor when pain still higher in belly area. Being able to hold still and curl your back like the letter.