First, you mention that theta is positive "even" if you are long, but it would "only" be positive if you are long as it must necessarily be negative if you are short.
If you want a mathematical explanation, go look up the formula for theta on Wikipedia. It's a straightforward calculation.
The intuitive explanation is the following:
Assume, for simplicity, S = 0.01, K = 100, vol = 20% (anything sufficiently small works), r = whatever, say 5%.
The value of the put is derived from its expected future payoff discounted at r. This put is so ridiculously in the money, however, that it will basically always be in the money regardless of expiry date. Since the price of the option is what it is worth today, and theta only really makes sense in valuing a European option, having to wait to get that $99.99 payoff sucks. The option is worth essentially $99.99 * e^(-rt) since the payoff is all but guaranteed and we only collect at expiration. Every day that passes reduces t, which increases the value of e^(-rt), which increases the value of the option. In situations where a put is extremely in the money, the American put is generally optimal to exercise rather than wait/sell for this very reason.