On his website, Arminian Perspectives, Ben Henshaw has a questions page at which he answers questions about Arminianism and Calvinism that visitors to his site pose in the comment section of the page. The following is a question and answer interaction between Ben and a commenter named Joseph:
Question: I used to consider myself a Calvinist but walked away from it once I understood what unconditional election, irresistible grace, and limited atonement really meant. I do believe that we are depraved and need a supernatural act of the Holy Spirit to enable us to respond to the gospel. I also do believe that once God saves you that you are His forever and that He will not let you become unregenerate again. What is the Armenian view on “once saved always saved”?
Answer: Just in case it wasn’t a typo, I should point out that it is “Arminian” and not “Armenian” (big difference). There is some debate over the issue of once saved always saved among Arminians. Arminius did not specifically declare himself one way or the other in his writings, though he seemed to lean in the direction of the possibility that true believers could fall away. Likewise, the Remonstrants (his followers) did not immediately declare themselves on the issue in their “Five Articles of Remonstrance,” but rather stated that it was an issue that required more investigation.
It wasn’t very long, however, before the Remonstrants did take a stand and argue forcefully for the idea that true believers can indeed fall away from the faith and that many do, in fact, fall away (you can find this in the “Opinions of the Remonstrants”). This has come to be the standard Arminian view, but one could call themselves Arminian and hold to once saved always saved since Arminius did not write anything definitive on the issue (he was more concerned with Calvinism making God the author of sin and taking the focus off of Christ in their decretal view of election).
Personally, I reject once saved always saved on exegetical grounds. If you want to read why I reject it you can check out my 13 part series on the topic:
https://arminianperspectives.wordpress.com/category/perseverance-series/