Mr Close was co-manager on the firm's £245m US Opportunities fund and sole manager on the US Mid Cap strategy.
Neptune has said it will shut the latter fund - only a year after it launched - with assets under management sitting below the £1m mark despite Mr Close having outperformed his peers and index.
His departure comes only a month after former US Opportunities fund manager Robin Milway left the company.
Mr Milway had replaced former head of US equities James Hackman, who left Neptune last September only four months after taking over from Felix Wintle.
Mr Close joined Neptune in 2013. He was promoted to co-manager on the flagship US Opportunities fund and given his own Mid Cap strategy in May 2016, following a restructure which saw head of US equities Mr Wintle leave.
The latest move now means its US Opps fund is run by Alistair Unwin - who became lead manager last month. George Boyd-Bowman, an income manager who took over Mr Hackman's £31m US Income fund last September, will help run the Mid Cap fund until it closes.
Mr Unwin also runs the firm's £10m Global Technology fund while Mr Boyd-Bowman is in charge of the £6.9m Global Income fund.
A Neptune spokesperson said: "[Mr Close] leaves with Neptune’s best wishes for the future.
"Neptune regularly reviews its fund range to ensure it meets the requirements of investors. The US Mid Cap Fund has attracted lower-than-expected investor demand and the costs associated with running the portfolio mean it is not in the interests of shareholders to continue."
The firm said all investors would be offered the chance to move into alternative Neptune strategies, and all costs covered by the company.