For me it depends on their durability and age and position.
For instance...Matt Holliday typically gets a day off when the suggestion pops up because he's older and I don't want him to injure himself. For Molina, I'll usually give him off 2 days a month and its typically on Sundays because they are day games following a Saturday night game. For everyone else, its basically how I feel at the time.
And no there is no way to check a player's energy during the game.