Why has my 11 month old Shih Tzu started urinating/defacating inside?

Question
My 11 month old female Shih Tzu has been house trained since about 3-4
months of age.

She initially was trained to sleep in her basket on the bedroom floor and
would wake me to go to the toilet. Unfortunately however we started having
her sleep on the bed. This went on for around 3 months. When I started
trying to train her to sleep in her basket again she started urinating and
defecating on the bedroom floor (always in the same place). I have now
moved her basket into a small cage where she now sleeps with no problems
and she is keeping her sleeping quarters clean.

This seems to be working however I am wondering if I will need to keep her
caged in forever or if there is a way to slowly leave the gate open and hope
that she will know not to go on the floor.

Also, 2 mornings this week after I have let her out and taken her outside I
have found that she has opted to urinate on the lounge room floor even
though the door is open and she could have gone outside. This is unusual
behaviour for her and I am wondering if it would have anything to do with her
being in the second week of heat?

Any information you could provide would be greatly appreciated.

Thank you.

Answer
Since you seem so new to the housebreaking issues, I'm wondering why you have an intact female at her age.  I hope you think about spaying her pretty immediately if you don't plan to show her in the breed ring.  I cannot be sure, but this sounds like sexually dimorphic or territorial behavior.  So, one thing that might help is to spay her.
If she is to be shown and bred (and I would not suggest you do the latter unless you do the former), then you will have to be more diligent in your supervision of her while she is indoors.  You can elect to tether the dog to your waist so that she cannot sneak off.  You then know when she is thinking about going, and can take her right out.  Reward her for urinating outdoors, but do not scold if she makes an error (some dogs just learn that pee'ing in front of the human is dangerous, so they sneak off to do it).  
Recommended reading:
http://www.petplanet.co.uk/petplanet/health/behaviour_urination.htm
http://www.amazon.com/Way-How-Housetrain-Dog-Any/dp/1891767089
http://www.morrco.com/noname1.html

Good luck!