You can force the menu items to remain visible in the secondary header on mobiles using this CSS:

@media screen and (max-width: 980px) {

#page-container {

padding-top: 0px !important;

}

#top-header {

position: static !important;

display: block !important;

}

#top-header .container {

padding-top: 0.75em !important;

}

#page-container #main-header {

position: relative !important;

top: 0 !important;

}

#top-header #et-secondary-menu,

#top-header #et-secondary-nav {

display: block !important;

}

#top-header #et-secondary-nav li {

text-align: center !important;

}

#et-main-area {

padding-top: 1px;

}

}