Persistent Core Animations (Swift 4.2). All you need is `self.layer.makeAnimationsPersistent()` 😎

CALayer+AnimationPlayback.swift

//
//  CALayer+AnimationPlayback.swift
//  Created by Philip Vasilchenko on 4/27/18.
//

import UIKit

//  Pause animations of layer tree
//
//  Technical Q&A QA1673:
//  https://developer.apple.com/library/content/qa/qa1673/_index.html#//apple_ref/doc/uid/DTS40010053

public extension CALayer {
    var isAnimationsPaused: Bool {
        return speed == 0.0
    }

    func pauseAnimations() {
        if !isAnimationsPaused {
            let currentTime = CACurrentMediaTime()
            let pausedTime = convertTime(currentTime, from: nil)
            speed = 0.0
            timeOffset = pausedTime
        }
    }

    func resumeAnimations() {
        let pausedTime = timeOffset
        speed = 1.0
        timeOffset = 0.0
        beginTime = 0.0
        let currentTime = CACurrentMediaTime()
        let timeSincePause = convertTime(currentTime, from: nil) - pausedTime
        beginTime = timeSincePause
    }
}

CALayer+PersistentAnimations.swift

//
//  CALayer+PersistentAnimations.swift
//  Created by Philip Vasilchenko on 4/27/18.
//

import UIKit

//  Persistent CoreAnimations extension
//  https://stackoverflow.com/questions/7568567/restoring-animation-where-it-left-off-when-app-resumes-from-background

public extension CALayer {
    static private var persistentHelperKey = "CALayer.LayerPersistentHelper"

    func makeAnimationsPersistent() {
        var object = objc_getAssociatedObject(self, &CALayer.persistentHelperKey)
        if object == nil {
            object = LayerPersistentHelper(with: self)
            let nonatomic = objc_AssociationPolicy.OBJC_ASSOCIATION_RETAIN_NONATOMIC
            objc_setAssociatedObject(self, &CALayer.persistentHelperKey, object, nonatomic)
        }
    }
}

public class LayerPersistentHelper {
    private var persistentAnimations: [String: CAAnimation] = [:]
    private var persistentSpeed: Float = 0.0
    private weak var layer: CALayer?

    public init(with layer: CALayer) {
        self.layer = layer
        addNotificationObservers()
    }

    deinit {
        removeNotificationObservers()
    }
}

private extension LayerPersistentHelper {
    func addNotificationObservers() {
        let center = NotificationCenter.default
        let enterForeground = UIApplication.willEnterForegroundNotification
        let enterBackground = UIApplication.didEnterBackgroundNotification
        center.addObserver(self, selector: #selector(didBecomeActive), name: enterForeground, object: nil)
        center.addObserver(self, selector: #selector(willResignActive), name: enterBackground, object: nil)
    }

    func removeNotificationObservers() {
        NotificationCenter.default.removeObserver(self)
    }

    func persistAnimations(with keys: [String]?) {
        guard let layer = self.layer else { return }
        keys?.forEach { (key) in
            if let animation = layer.animation(forKey: key) {
                persistentAnimations[key] = animation
            }
        }
    }

    func restoreAnimations(with keys: [String]?) {
        guard let layer = self.layer else { return }
        keys?.forEach { (key) in
            if let animation = persistentAnimations[key] {
                layer.add(animation, forKey: key)
            }
        }
    }
}

@objc extension LayerPersistentHelper {
    func didBecomeActive() {
        guard let layer = self.layer else { return }
        restoreAnimations(with: Array(persistentAnimations.keys))
        persistentAnimations.removeAll()
        if persistentSpeed == 1.0 { // if layer was playing before background, resume it
            layer.resumeAnimations()
        }
    }

    func willResignActive() {
        guard let layer = self.layer else { return }
        persistentSpeed = layer.speed
        layer.speed = 1.0 // in case layer was paused from outside, set speed to 1.0 to get all animations
        persistAnimations(with: layer.animationKeys())
        layer.speed = persistentSpeed // restore original speed
        layer.pauseAnimations()
    }
}

LICENSE

Copyright 2018 Philip Vasilchenko

Permission is hereby granted, free of charge, to any person obtaining a copy of this software 
and associated documentation files (the "Software"), to deal in the Software without restriction, 
including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, 
and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, 
subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial 
portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT 
LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. 
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, 
WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH 
THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

@warpling, thanks for the notice.

Code updated for Swift 4.2