Apart from the suspicions of leading military officers, the other major problem facing Richard was a financial crisis. He decided to call a Parliament to find a resolution to the economic problems but due to his lack of influence on the election, the voters returned a majority of moderate candidates. Some MPs secretly wanted a restoration of the monarchy.
Parliament and army were soon at odds, with Cromwell in the middle. The army petitioned for increased taxation to ensure that soldiers were paid. Parliament responded by passing legislation that army officers could not assemble without permission of the Lord Protector. The affronted army officers demanded that Cromwell dissolver parliament. When he refused they sent troops to St. James’s Palace (where Parliament met). Richard eventually relented, dismissed the Third Protectorate Parliament and recalled the Rump Parliament.
Richard’s position had become untenable. He accepted parliamentary calls for his resignation on 25th May 1659 in return for the settlement of his debts and payment of a pension. The power vacuum that the resignation created resulted in the eventual restoration of the monarchy in 1660. That year Richard Cromwell left for France under the assumed name ‘John Clarke’. His exile lasted for twenty years, after which he quietly returned to England. Initially, he lodged with a merchant in Finchley, Middlesex (now in London) and then moved to Cheshunt, Hertfordshire where he lived until his death in 1712.
David Plant’s informative British Civil Wars site includes a biography of Richard Cromwell.