Is the Chin Not As Strong with an Implant in Place?

Without an exam your question cannot be answered.  You will need to see an Oral/Maxillofacial surgeon to see if othognathic surgery, genioplasty or using an implant is best for your specific case. It should be noted that patients with severely weak jaws or abnormally functioning jaws may be better treated with other facial surgery (orthognathic surgery), although a chin augmentation may be an option at a later time. These patients should seek the advice of a plastic surgeon to determine which course is right for them. Here is some information to help you make this decision: Candidates for Chin Augmentation - Patients whose chin profiles are weak but have normally functioning jaws are candidates for Chin Augmentation. Many of these candidates have used injectable fillers in the past to strengthen the protrusion of their chins, but are looking for a permanent solution. If you are one of these patients, then you are a likely candidate for chin augmentation

after a few months when scar tissue has formed a capsule over the implant it is nearly as strong as before

This really depends on the makeup of the implant. Implants can be fabricated from silicone gel, PTFE, Porous polyethylene, woven polypropylene mesh, hydroxyapatite, bone, etc.
Depending on the composition of the implant it is possible that it can fracture or break. However, the vast majority of implants will not break and are quite durable.
Discuss your implant concerns with your surgeon and make sure you are well aware of the brand, size, shape and composition.

Depending on what your surgeon likes to use, chin implants can be flexible (silicone) or solid with characteristics similar to plastic. None of these are particularly brittle. The flexible ones can withstand a lot of blunt trauma (your skin will get damaged long before the implant will). In the case of the more rigid implants, I would think that any force strong enough to crack the implant would probably cause a jaw fracture as well.
It is possible to have a chin augmentation without using a synthetic implant (splitting the bone and moving a segment forward). In this case, right after the surgery you would be at higher risk for a jaw fracture from a fight. Depending on how much bone overlap and callous formation is expected, in the long term your jaw could be weaker, the same, or stronger. (Discuss this with your surgeon.)
I hope that helps.