Was American independence from Britain inevitable?

It is difficult to say to that any event is truly inevitable, especially when potential counterfactuals are taken into account. In this case, we would need to determine whether America would have obtained its independence either absent the Revolutionary War or in spite of a loss in the Revolutionary War. American independence was a likely event, though it would have taken longer. Trends at the time would likely have led America down a path similar to that followed by Canada, which ultimately led to a peaceful independence from Britain. However, some of the trends that led to Canadian independence may not have been present had America not gained its independence, making it difficult to determine the inevitability of American independence.
Canadian independence largely came out of issues in resolving conflicts between French and British colonists concerning claims to various land holdings, a desire for a common defense among Canadian settlers, a desire for a national railroad, and the confederation of various colonies based around mutual benefit. In the absence of the Revolution, it is likely that the American colonies would also have entered into some form of confederation based on mutual benefit and would also likely have desired a national railroad. Conflict with the French would also have remained, though the French would likely have maintained a stronger hold on their territories because they would not have faced the financial difficulties caused by aiding the American Revolution. This may have undermined the cause for independence, as a newly independent nation would have more difficulty defending itself against the French. The need for a common defense would also likely have remained, though it would have been focused on defense against the French, as American aggression against Canada would likely not have been a concern.
In the event of a failed American Revolution, the same issues would likely have been present, though the threat of the French would depend on France's involvement in the American Revolution. In both scenarios there is also a need to account for the French Revolution, which may not have occurred without the American Revolution. A failed American Revolution, especially one in which France did not participate, would likely have undermined the cause of the French Revolution.
Regardless, it is likely that America would have gained independence from Britain without the American Revolution; however, this would likely not have happened until the late 1800s, and America may have been included in the nation of Canada (though only the eastern seaboard would have been incorporated). The disposition of the western parts of the American continent, as well as Florida, are uncertain.