Why does Android WebView sporadically not sending my session cookie?

Thanks justingrammens! That worked for me, I managed to share the cookie within my DefaultHttpClient requests and WebView activity:

//------- Native request activity
private DefaultHttpClient httpClient;
public static Cookie cookie = null;

//After Login
List<Cookie> cookies = httpClient.getCookieStore().getCookies();
for (int i = 0; i < cookies.size(); i++) {
    cookie = cookies.get(i);
}

//------- Web Browser activity
Cookie sessionCookie = myapp.cookie;
CookieSyncManager.createInstance(this);
CookieManager cookieManager = CookieManager.getInstance();
if (sessionCookie != null) {
    cookieManager.removeSessionCookie();
    String cookieString = sessionCookie.getName() + "=" + sessionCookie.getValue() + "; domain=" + sessionCookie.getDomain();
    cookieManager.setCookie(myapp.domain, cookieString);
    CookieSyncManager.getInstance().sync();
}