It appears that you have bindweed, hard to tell from these photos if it's field bindweed (Convolvulus arvensis L.) and hedge bindweed (Calystegia sepium). Both are perennial vines with extensive root systems and their management will be the same. 

Management of bindweeds can be very difficult, in addition to their extensive root systems, they respond to disturbance by creating more shoots, and seeds can survive for decades in the soil.

In this publication you'll find a list of herbicides that can be applied, but it's recommended that you use a combination of mechanical (hand-pulling, be sure to bag and throw away the plant tissues), cultural (smothering with thick mulch) and chemical controls. Best control is achieved in late summer for good translocation to roots.

https://ipm.ucanr.edu/PMG/PESTNOTES/pn7462.html

Please also be aware that many of the chemicals that are now sold as "Round Up" are no longer made with Glyphosate, what used to be the active ingredient in Round Up. Check the label of the product you've been using to be sure that it indeed is Glyphosate. Please also know that Glyphosate take about 2 weeks to be effective. Some folks do not wait long enough to see results and spray again, which might have adverse effects on other plants nearby. Always follow the label with using chemicals.

https://www.canr.msu.edu/news/avoid-herbicide-misuse-at-home-things-to-know-before-you-buy