I have the same problem on 8.4.1 . I was running iOS 5 before (yes you read that right), which did not behave like this.
To those who say it is not a problem, and that it works as intended... I'm sorry this isn't how a multi-tasking device is supposed to behave. No other multitasking computer OS I have ever worked with has ever acted like this.
I'm not running a whole lot of apps either: the basics (phone, message, calculator, camera) plus Safari (with 2-3 tabs) and on occasions Google Maps.
Since the problem did not exist on iOS 5 (nor on iOS 6, if I go by the various reports on this thread) either it's a bug, or Apple have decided it is a good idea to make running apps drop part of their memory when the phone gets low on RAM to overcome how bloated and RAM-hungry iOS has become.
In any case, it is totally frustrating.
What's even worse: due to Apple's overly restrictive policies and iOS signing dictatorship, I cannot revert back to iOS 5 or 6.
So I'm SOL.
P.S.: Just to make it clear, I'm not an Apple hater. While I much prefer PC's to Macs and Windows (even 10) to OS X in general, one thing that I am NOT is a fanboy : I give credit when credit is due and I criticize when criticism is due.
iPhones are nice pieces of hardware.
P.P.S.: Please avoid troll-posting / post responsibly. Posts that imply that one can buy a different device if one is not satisfied are pointless and bring no solution. Not to be rude, but please don't bother posting such meaningless comments.