I might need to correct myself a little on this. Arminius perhaps believed, rather, that some of the elect could actually be lost, as he draws a distinction between believers and the elect. Though it hard to discern exactly what he means by this, it does seem to appear he believes one can lose their salvation.
Since election to salvation comprehends within its limits not only faith, but likewise perseverance in faith; and since St. Augustine says, “God has chosen to salvation those who he sees will afterwards believe by the aid of his preventing or preceding grace, and who will persevere by the aid of his subsequent or following grace; “believers and the elect are not correctly taken for the same persons. Omitting, therefore, all notice of the word “election,” I reply, believers are sometimes so circumstanced, as not to produce, for a season, any effect of true faith, not even the actual apprehension of grace and the promises of God, nor confidence or trust in God and Christ; yet this is the very thing which is necessary to obtain salvation. But the apostle says, concerning faith, in reference to its being a quality and a capability of believing, “some, having cast away a good conscience concerning faith, have made shipwreck.” (emphasis mine)
This was part of an historical exchange Arminius participated in with the Deputies of the Synod in the early 1600s. Fascinating debate thread (if you will).
Jacob Arminius founds Arminianism | Christian History Institute
I do like many of the things Arminius said. Arminianismts today don't seem to argue like he did. I also see where the Scriptures do seem to speak of believers falling way, but in context these are always false believers—tares, who never produce fruit—Christians by proxy.