A friend of mine took a similar view when someone was raiding his till. He sprang a trap to 'catch' the culprit (he already knew who she was), then backed off from sacking her or taking any action at all because he felt sorry for her. She was a single mum with small children.
Over time, her thieving continued, and he tried to justify his actions to himself and his wife by claiming that the employee was vital to the business and contributed more to it through her hard work and loyalty than she was stealing from it.
He lost a total of £50,000, and was further penalised because the taxman disbelieved his low profits.
My friend is an admirable person, and I'm sure you are too. However, you're both mugs.
You have to confront the employee in question. If you're worried about doing this on your own, get someone else involved too. You can handle the matter sensitively and compassionately - if there are mitigating circumstances, these can be taken into account. You don't have to involve the police if you don't want to, You can even (more fool you, in my opinion) give them another chance.
But what you mustn't do is to allow this to continue. It's not good for you, your business or, quite frankly, the person who has his or her hand in the till.