The color picker is missing the || document.observe('xwiki:dom:loaded', init) half. So when the RequireJS callback resolves beforexwiki:dom:loaded has fired, init() is never called and nothing will ever call it again. The inputs still render (they are server-side HTML produced by #colorPicker_input in flamingo/macros.vm) but stay plain text fields with an empty grey swatch — exactly what the attached screenshot shows. It also explains why there is usually no error in the JavaScript console.
Why the race flips from one page load to the next
colorPicker.js is pulled in by #colorPicker_import in flamingo/macros.vm via $xwiki.jsfx.use('colorPicker.js', true), so it is emitted as a deferred script tag inside the #javaScriptExtensionHooks block of flamingo/javascript.vm.
Deferred scripts execute in document order as soon as they are available, but DOMContentLoaded only fires once the last one has run. At least compatibility.js and markerScript.js come after the extension hooks block, plus the theme page's own JSX (FlamingoThemesCode.ThemeSheet, FlamingoThemesCode.LessCodePluginJs).
XWiki.domIsLoaded is only set at the very end of that chain: dom:loaded -> XWiki.initialize() -> xwiki.js. And initialize() postpones itself once more if markerScript.js has not run yet.
Meanwhile require(['jquery', 'colpick'], ...) has already started loading asynchronously. When jQuery is already resolved and colpick is served from the browser HTTP cache, that callback can easily land inside the window during which the remaining deferred scripts are still being downloaded. At that moment XWiki.domIsLoaded is still false, so the pickers are silently skipped.
That is why the bug depends on the browser cache, on the number and weight of the scripts on the page and on the browser's script scheduler (reproduced easily on Chrome/Edge, rarely on Firefox), why repeated refreshes keep reproducing it (a warm cache keeps winning the race), and why it eventually "fixes itself".
Secondary defect in the same file
colorPicker.js uses jQuery to listen for xwiki:dom:updated, but it does not require xwiki-events-bridge. That module is only declared as a RequireJS path in flamingo/javascript.vm, it is not loaded by default, and it is what forwards Prototype-fired xwiki:* events to jQuery listeners. Compare with localePicker.js, which does require it. So even the xwiki:dom:updated fallback only works when some other module happens to have loaded the bridge.
About the two console errors in the screenshot
Both look like red herrings for this particular bug:
Uncaught ReferenceError: Effect is not defined (ModalBox:519) — a dom:loaded handler using script.aculo.us' Effect without require(['scriptaculous/effects']). Prototype fires custom events through dispatchEvent, so the browser isolates the exception and the remaining dom:loaded handlers (including XWiki.initialize) still run. ModalBox does not exist anywhere in xwiki-platform, so it comes from an extension installed on that instance. It is a genuine bug, but a different one.
The 404 on .../skin/skins/flamingo/resources/js/scriptaculous/scriptaculous.js — that is the legacy path; script.aculo.us is a WebJar RequireJS package now. A slow or failing request in the deferred script chain is however a good aggravator: it widens the DOMContentLoaded window and makes the race described above much more likely.
Fix
Register the xwiki:dom:loaded listener unconditionally (safe: if the DOM is already loaded the event will not fire again, so there is no double initialization), and require the events bridge: