How Long Can Ruptured Saline Implants Stay in my Body?

I agree with the answer below- tightening of the connective tissue pocket around your implant will progress with time.
While this is possible to improve at surgery, the chances of you achieving an excellent outcome and symmetry are higher if you have this managed sooner rather than later.
Having said that, there should be no risk to your health if you are unable to deal with this immediately.

It cannot cause harm.  It is in fact no different now than it was when it was full of saline.   The pocket may close and it may be difficult to retire your breast shape if you wait too long, but the implant shell itself won't harm you.

It's best to replace a ruptured saline implant within the first month after the rupture. If you wait longer, the overlying skin and the capsule around the implant will begin to shrink. It becomes more difficult to perform the surgery and to get good symmetry when the implant has been ruptured for a long time.

In my practice, I do not recommend leaving any ruptured or compromised implant device in a patient for any extended period of time.  I recommend and prefer replacing a ruptured implant immediately (or as early as possible) as the capsule, or layer of scar tissue that surrounds the implant, will begin to shrink down and tighten around the compromised (deflated) implant making replacement of the implant a more involved procedure.  If for personal reasons you are unable to take care of this deflation right away, there is no real risk to your personal health as the saline can be easily absorbed by the body.  But keep in mind that leaving this deflated implant for an extended period of time can potentially compromise the final cosmetic result when you are in fact able and ready to undergo an implant exchange.    

A ruptured saline implant will not cause injury or illness and does not need to be removed with haste.  It would typically be quite safe for you to have the ruptured implant in your body for some time until it is convenient to have it removed and replaced.  

It is advised to get deflated implants removed as soon as you notice the rupture because it makes replacement easier. However, if it's been a while and you haven't noticed any problems, it's fine to keep them until you do have a chance to have them removed or replaced.