In general, you don't have any obligation to enforce your rights.
There is the well-known exception of trademark law, but that's in the nature of the matter. If PepsiCo sells Coca-Cola and the Coca-Cola company doesn't react, then the trade mark obviously doesn't allow customers to identify genuine Coca-Cola.
Your example seems a bit off. Yes, Coca-cola is not required to enforce their trademark via legal means; however, they may lose the ability to prove infringement of the mark later (even in another case) if they do not police use of the mark. I think there was also a case or course of legal thought by some judges that the mark's owner owed a duty (fiduciary maybe?) to actively protect the mark from infringement or risk losing the trademark rights altogether.
Theoretically no, but the court is more likely to side with you if your lawyer can go down the list checking off each reason this lawsuit is like the last one that you won.
There is the well-known exception of trademark law, but that's in the nature of the matter. If PepsiCo sells Coca-Cola and the Coca-Cola company doesn't react, then the trade mark obviously doesn't allow customers to identify genuine Coca-Cola.