This sounds like Gummy Stem Blight


see here http://vegetablemdonline.ppath.cornel...

"Gummy stem blight, caused by the fungus Didymella bryoniae as the sexual stage (perithecia giving rise to ascospores) and Phoma cucurbitacearum as the asexual stage (pycnidia producing conidia), is a common disease of all major cucurbits and is present wherever they are grown. Both stages of the pathogen can occur on infected tissue during the season, but they vary in importance as inoculum sources."



Cultural Control

Disease-free seed should be used for all cucurbit plantings. Obtain seed from reputable sources. If seed is to be saved from open-pollinated varieties, these should originate from disease free plantings and should be harvested at a location where there is no contamination by airborne conidia. Use of seed disinfectants does not guarantee that all seed is disease-free. Seed disinfectants are more effective when used as solutions or suspensions than as dry dust treatments. To be safe, growers should follow a minimum 2-year rotation out of all cucurbits. To encourage decay of plant debris, crop refuse should be plowed under as soon as possible after harvest. Powdery-mildew-resistant (PMR) cucumber and muskmelon varieties should be grown to reduce the opportunity for gummy stem blight infections. PMR pumpkin and summer and winter squash will be available soon. Cucumber beetles and aphids should be controlled to reduce predisposing cucurbits to disease.


Note
"Older leaves turn brown and die and the entire plant may die as the disease progresses. A fungicide containing chlorothalanil may arrest it but as with most plant diseases, control is very difficult. Crop rotation might help with both possibilities next year"
http://www.americangourdsociety.org/b...

Also, see here https://www.apsnet.org/publications/a...