In fruit Ninja classic mode, sometimes you can gain strikes back. How/when does this happen? It has been indicated that it might be on critical strikes, but I can confirm that this is at least not always the case - I've gotten critical strikes and no strikes back.
You can also slice a Dragon Fruit to get one of your Strikes back. Use the "Dragon Blade" to replace the Pomegranate with Dragon Fruit, or wait for the "Ultra Rare" Dragon Fruit only appearing in Classic Mode. I only ran into the "Ultra Rare" Dragon Fruit once so using the "Dragon Blade" is the best way. In Arcade, the "Dragon Blade" replaces the Pomegranate with four Dragon Fruit which you can usually slice as a "Four Fruit Combo", while in Classic each Pomegranate is replaced by one Dragon Fruit which you slice to get one of your Strikes back.