George Orwell declared that "language does not reflect culture; language is culture." This statement indicates that Orwell realizes that there are no set "rules of grammar," that languages change throughout time. However, many of the changes are in sentence length, phrasing, and other minor alterations which do not affect the basic structure of the language.
While many argue against stringent "rules," there is a necessity to have a standard for every language so that people who learn new languages have guidelines, and so that the language of a people does not change so much that people can no longer understand each other.
The hard part of interpreting the phrase "the rules of grammar" is that it is used by both prescriptivist and descriptivist thinkers. Prescriptivists tell us how we should use language, and sometimes their prescriptions change the way we do use language. A good example of a prescriptivist is Bishop Robert Lowth, who in the 1700s simply decided that English should conform to the rules of Latin. He invented rules like the one about not using double negatives and the one about not splitting infinitives. Before Lowth, educated speakers did both those things, but now we are taught not to do them.
Descriptivists describe the way we do use language, setting aside any rules about how we should use it. Nevertheless, descriptivists talk about the rules of language almost as much as prescriptivists do. Stephen Pinker is a descriptivist. In his book Words and Rules, he describes the way language rules come about naturally as our brains make patterns with words. Pinker dismissed many of the rules we learn in school, instead focusing on rules we make naturally.
Let's look at it like this. Rules are there for a reason, and with regard to grammar, the rules are there because in our day and age this is how language makes the most sense. Yes Shakespeare did things a certain way, but the rules of grammar have not changed for a long, long time. The rules seem to change more as a means of placating a society that gets lax about the rules.
I think the rules of grammar are subject to change as society and its use of language, both written and spoken, change. Many of the rules have not been changed over time, but some of them have been modified as the culture changes.
When someone writes "rules of grammar," they are generally not being descriptive but rather prescriptive. The word "rule" suggests that there are set guidelines, against which each statement or written sentence can be measured as right (it follows the rule) or wrong (it breaks the rule). I would expect a descriptivist approach to use less rigid terms, such as "pattern" or "tendency" or "trend" or "system" or even "usage" or "schemata."
Rules of grammar (in a prescriptivist sense) definitely change over time. Double negatives were perfectly fine in Early Modern English (Shakespeare uses them!), and common nouns were often capitalized if a writer felt like capitalizing them. Today, we're told that the rules of grammar forbid double negatives (although many people still use them) and dictate that only proper nouns should be capitalized.
That fact that these "rules" of what is right and what is wrong change, I think, undermines the very notion that we can clearly define what is good grammar and what is bad grammar. The prescriptive rules in English often fail from the start; many of these rules were grounded in what was considered good grammar in Latin and Greek. "Never end a sentence with a preposition" is an example of variance because Germanic languages end sentences with prepositions all the time.
Of course, if you view "rules of grammar" in a descriptive way, it's probably fair to say that the rules can change but don't change much. In the course of the development of English (from 450 AD to the present), we've simplified but not gotten rid of noun and pronoun inflections, for example, and subjects and verbs still generally have to agree.
Rules of grammar are certainly changeable over time -- I believe that linguistics and grammar rules are descriptive and not prescriptive. The rules should only describe what things are like at a given time -- they should not say how things must be forever more. This was especially true before languages were written, but it is still true.
You could follow this link for a discussion of some seeming changes in English grammar in contemporary times.