how do I stop a website from automatically logging me out when I'm using cypress?

What you should know is that Cypress clears the state of browser every time it starts a new it(). So something what is done in the first it() is not now in the second it(). In your case, the login is in the first it, in the second it the application is not logged in anymore. To take care that Cypress stays logged in, you should move the login step to a before() or a beforeEach() (depends wether you want to login once per describe or per every it.

Following your post it seems you like it to login once and stay logged in, so the before() does the job for you. Your code would look like this:

describe('signing in', function() {
  before('Logijn to the application', function() {
    cy.visit('https://testing.safeandreliable.care/sign-in')
    cy.get('[id="at-field-username_and_email"]').type('bcramer@safeandreliablecare.com')
    cy.get('[id="at-field-password"]').type('******')
    cy.contains('Sign In').click()
  })
  it('signs into the default entity', function(){
    cy.get('[id="help-text-board"]').click({force:true})
    cy.wait(9000)
  })
  it('next test', function () {
    // do other test but still logged in
  })
})

You need to add the following (among with the other changes proposed in https://stackoverflow.com/a/56593040/8928727):

beforeEach(() => {
        Cypress.Cookies.preserveOnce('whatever session id')
    })

If the above is missing you would still have your cookies deleted between tests, and in this case that's not what you want. Read more here: https://docs.cypress.io/api/cypress-api/cookies.html#Preserve-Once