Let me be very clear:
God is still a healing God! In an age where people tend to be skeptical about everything (and Christ-followers are not immune to this skepticism), we can know that God is still the same HEALER that He has always been.
Now, a few questions:
1) Does God hear every prayer for healing? Of course.
2) Does God answer every prayer for healing? Yes. He often says "yes" and He often says "no" and sometimes He will even say "wait." But God does answer the prayers for healing. We just may not get the answer that we want, when we want it.
3) How do I know that God heals today? His Word tells me that Christ is the same "yesterday, today, and forever." Christ healed many, many who came to Him--and He hasn't changed. I either believe His promises about Himself, or I don't.
4) Didn't the "miraculous" end when the Biblical Canon was completed? No. The Holy Spirit didn't leave us...and we are not second-class citizens of God's family. God, and God alone decides when, where, how, and why He will perform His mighty works--including salvation, healing, and any other miraculous act He chooses to perform.
God still heals people....and let's always ask Him, believe Him, and trust Him.
Even when He says "no."