From a purely Biblical perspective, there is nothing in God's word that promises that we will not suffer. In fact, it teaches the opposite.
From a tract put out by Living Waters Publications:
It is true that God loves you, but you decide if His plan is
"wonderful." If you have heard that happiness comes through Jesus
Christ, you may like to think again. The first thing Jesus said of the
Apostle Paul (who wrote most of the New Testament) was that He would
show him "how great things he must suffer for (His) name's sake.1
Three times Paul was beaten with rods, once he was stoned, three times
he suffered shipwreck, a night and a day he spent in the sea. There
were times when Paul was so unhappy, he wanted to die.2
The Bible says, "All who live godly in Christ Jesus shall suffer
persecution."3 It says we enter the Kingdom of God through much
distress,4 and that we were appointed to afflictions.5
Jesus said if we followed Him we would be reviled, persecuted, hated,
and all manner of evil would be said against us falsely, for His sake.
He warned that we would have to take up our cross daily, deny
ourselves and follow Him, saying, "In the world you shall have
tribulation," and even that we may be called to die for our faith.6
That is 100% true. Being delivered from Evil is a valid prayer request, but we understand that it doesn't mean we will always be delivered. Someone on this site recently said "God isn't some Genie that goes around granting wishes." That's also 100% true.
The question appears to come from the perspective that "God has a wonderful plan for your life" and also a variation of the Prosperity Doctrine (where all our evils are caused by our own sin, but if we are just, we'll get whatever we desire).
I've always had a problem with both teachings. For a more lengthy discussion on the topic, I recommend Ray Comfort's book on the topic, freely available online in pdf format.
Some relevant verses:
(Mark 8:34-36) If anyone would come after me, let him deny himself and take up his cross and follow me. For whoever would save his life
will lose it, but whoever loses his life for my sake and the gospel’s
will save it. For what does it profit a man to gain the whole world
and forfeit his soul?
(Acts 9:15-16) But the Lord said unto him, Go thy way: for he is a chosen vessel unto me, to bear my name before the Gentiles, and kings,
and the children of Israel: For I will shew him how great things he
must suffer for my name's sake.
(John 15:18-21) If the world hates you, you know that it hated Me
before it hated you. If you were of the world, the world would love
its own. Yet because you are not of the world, but I chose you out of
the world, therefore the world hates you. Remember the word that I
said to you... If they persecuted Me, they will also persecute you...
because they do not know Him who sent Me.
Also, the book of Job is a pretty good example of someone that God loves, suffering because God allowed it. We are reminded in that story that God is sovereign, and that He allows suffering for His purposes.
Suffering increases faith, encourages reliance on God, and destroys pride. In short, pain makes you stronger and better. It refines us as a fire refines fine metals:
Behold, I have refined thee, but not with silver; I have
chosen thee in the furnace of affliction.
So, in short, when we see Believers not "delivered from Evil" we don't think it's unnatural. And we darn well should be thinking "what can I do to provide comfort or help".